AD-Ai5I 17S EMPLOYMENT OF ADAPTIVE LEARNING TECHNIQUES FOR THE L/2DISCRIMINATION OF RCOU..(U) GENERAL ELECTRIC CORPORATERESEARCH AND DEVELOPMENT SCHENECTA. J W ERKES ET AL.
UNCLASSIFIED DEC 84 945RD882 N09914-82-C-293i F.'G 20/1 N
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EMPLOYMENT OF ADAPTIVE LEARNING TECHNIQUESFOR THE DISCRIMINATION OF ACOUSTIC EMISSIONS
o J.W. Erkes and K.C. Tam S
General Electric Corporate Research and DevelopmentV'"
S.R. Mannavao General Electric Turbine Technology LaboratoryLn S
J.F. MacDonald and H.A. ScartonRensselaer Polytechnic InstituteI
PHASE II FINAL REPORTContract N00014-82-C-2031
December 1984
Prepared by DTIC .
J.W. Erkes, Project Manager ELECTEGeneral Electric Company
Corporate Research and Development FEB12M5Schenectady, New York 12345 U
BPrepared for
H. Chaskelis, Project ManagerNaval Research Laboratory
L 4555 Overlook Avenue, S.W.Washington, DC 20375
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Washington, DC 2037511. TITLE IInciUde security Classification' Employment of Adaptive Learning
Techniques for the Discrimination of Acoustic Emissions (Unclassified)
12. PERSONAL AUTNORISI Erkes, J.W.; Tam, K.C.; Mannava, S.R.; MacDonald, J.F.; Scarton, H.A. . - -13& TYPE OF REPORT 13b. TIME COVERED 14, DATE OF REPORT (Y,. MIo.. Day, 15. PAGE COUNT .
Phase II Final Report FROM Nov 82 TO Nov 83 December 19841-. SUPPLEMENTARY NOTATION
17 COSATI COCES 18. SUBJECT TERMS ,Continue on reverse itf necesSarY and identify by block numbep,
FIELD GROUP sue. GR. " Acoustic Emission, Digital Signal Processing, Adaptive Learning, - - -
Homomorphic Deconvolution•• .
19. ABSTRACT tContinue on reverse if necessary and identify by blol numberl
Under Phase I of this contract, several new acoustic emission techniques were developed. These techniques]showed promise as a means of adaptively learning and removing multimode and multipath effects from acoustic em- -ission signals in a preprocessing step prior to source characterization. In this Phase 1I effort, software was developedto implement the techniques, and a series of experiments was carried out to assess the effectiveness and practicalityof these techniques on real signals. Analysis of the data revealed that reasonably accurate transfer functions could .7.
be determined adaptively, when a flat response wide-band transducer was employed, and when relatively shortrecord lengths were used. Available commercial transducers with the requisite frequency response are quite fragile,however, and are far too insensitive for practical use. Pattern recognition techniques were also explored as a means - -of characterizing acoustic emission sources; specifically, details of the pulse microstructure were examined for evi-dence of characterizable features. No such evidence was found in either "raw" (reverberation dominated) or pro- - .,-
cesseddata. C , I. , , - . L ./ ' " '. , -.
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H. Chaskelis (202) 767-3613
00 FORM 1473, 83 APR EDITION OF I JAN 73 IS OBSOLETE. UnclassifiedSECURITY CLASSIFICATION OF THIS PAGE
......................................... ,.........,...... .. .' ,.'.'..',','.,.. .. ,..... .- ..... -. ., ." . ... ... .., .
7-7;L 77 -
TABLE OF CONTENTS
Section Page
I INTRODUCTION AND SUMMARY........................................................ 1-1
1.1 Introduction.............................0.................................................. 1-11.2 Signal Processing ......................................................................... 1-1
kv ~1.3 Sensor Evaluation ........................ 0................................................ 1-21.4 Experimental Confirmation ............................................................. 1-21.5 Summary............................................................ 0...................... 1-2
2 THE THEORY REVISITED .................................................................. 2-1
2.1 Generalized Time Distribution Functionfor Multiple-Event Waveforms ......................................................... 2-1
2.2 Single-Event Approximation............................................................ 2-12.3 Multiple Events........................................................................... 2-2
2.3.1 Multiple Events with Occasional Single Events................................ 2-22.3.2 Overlapping Multiple Events .................................................... 2-2
2.4 Exponential Weighting................................................................... 2-42.5 Bandpass Mapping........................................................................ 2-7
3 EXPERIMENTAL APPARATUS............................................................. 3-1
3.1 Hardware.................................................................................. 3-23.1.1 Specimens ............... ......................................................... 3-23.1.2 Transducers ....................................................................... 3-33.1.3 Analog Signal Conditioning Equipment ........................................ 3 -33.1.4 Transient Waveform Recorders................................................. 3-33.1.5 Stress-Corrosion Event Monitor................................................ 3-4
3.2 Software .................................................................................. 3-43.2.1 Data Acquisition .................................................................. 3-43.2.2 Analysis ........................................................................... 3-5
4 EXPERIMENTAL RESULTS................................................................. 4-1
4.1 Calibration ................................................................................ 4-1*4.2 Effect of Record Length................................................................. 4-4*4.3 Dependence on the Width of the Cepstral Filter ..................................... 4-6
4.4 Dependence on Alpha.................................................................... 4-64.5 Fourier Deconvolution .................................................................. 4-94.6 Effects of a Limited-Frequency Band................................................... 4-144.7 Pattern Recognition ...................................................................... 4-16
5 CONCLUSION .................................................................................. 5-
6 REFERENCES.................................................................................. 6-1
TABLE OF CONTENTS (Cont'd)
Section Page-. APPENDIX A - BIOMATION 8100 DR11-C INTERFACE A-I
6APPENDIX B - ILS SOFTWARE MODULES B-I
APPENDIX C - PATTERN RECOGNITION SCATTER PLOT PRODUCTION C-1
DTICELLCTFEB 12 1985
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.uit J tion
Distribution/
Availability CodesAvail anid/or
Dist SpecialAll
iv
LIST OF ILLUSTRATIONS
Figure Page
1 The delta-shaped time distribution function obtained by averaging the timedistribution function of a large number of multiple-event waveforms with one ... ,..
of the events in each waveform aligned ........................................................................... 2-4
2 The relation between record length and frequency sampling interval ............................ 2-5_0
3 Removing zeroes in z-transform by exponential weighting ............................................. 2-6
4 Modified homomorphic characteristic system including exponential weighting ............. 2-6
5 Bandpass m apping operation ............................................................................................. 2-7
6 Characteristic system for bandpass homomorphic systems ............................................. 2-8
7 Block diagram of the data acquistion system .................................................................... 3-1
8 The experimental setup, showing the thick test plate, the Biomation transientrecorders, the analog instrumentation, and VAX 11/750 control/analysis computer .... 3-2
9 A typical lead-break waveform recorded by a NBS conical transducer ........................... 4-210 Another lead-break waveform recorded by a NBS conical transducer located
54 cm from the one used in Figure 9 ............................................................................... 4-2
11 The cepstrum of the waveform in Figure 10 ............................... 4-3
12 The result of low-time pass filtering the cepstrum of the waveform in Figure 10 ......... 4-4
13 The improved result obtained through the use of exponential weighting; a - 0.9955 4-5
14 The theoretical seismic surface pulse according to Pekaris .............................................. 4-6
15 A lead-break waveform recorded by a NBS conical transducer located 45 cm* from the source .................................................................................................................. 4-7
16 A lead-break waveform recorded by a NBS conical transducer located 45 cmfrom the source ................................................................. .............................................. 4-7
17 A lead-break waveform recorded by a NBS conical transducer located 30 cmfrom the source .................................................................................................................. 4-8
18 A lead-break waveform recorded by a NBS conical transducer located 15 cmfrom the source .................................................................................................................. 4-8
19 The result of low-time pass filtering the cepstrum of the waveform in Figure 15,-'using all of the 8096 samples as input; a 0.9985...........................................4-.9
20 The result of low-time pass filtering the cepstrum of the waveform in Figure 16,using all of the 8096 sam ples as input; , - 0.9985 .......................................................... 4-10
21 The result of low-time pass filtering the cepstrum of the waveform in Figure 17,using all of the 8096 sam ples as input; a - 0.9985 .......................................................... 4-10
22 The result of low-time pass filtering the cepstrum of the waveform in Figure 18,using all of the 8096 samples as input; a - 0.9985 .......................................................... 4-11
V
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LIST OF ILLUSTRATIONS (Cont'd)
Figure Page23 The result of low-time pass filtering the cepstrum of the waveform in Figure 15,
using only the first 2048 samples as input; a - 0.9985 .................................................... 4-12
24 The result of low-time pass filtering the cepstrum of the waveform in Figure 16,using only the first 2048 samples as input; a - 0.9985 .................................................... 4-13 '
25 The result of low-time pass filtering the cepstrum of the waveform in Figure 17,using only the first 2048 samples as input; a - 0.9985 .................................................... 4-13
26 The result of low-time pass filtering the cepstrum of the waveform in Figure 18,using only the first 2048 samples as input; a - 0.9985 .................................................... 4-14
27 The result of low-time pass filtering the cepstrum of the waveform in Figure 10, "a - 0.999, width of cepstral filter - + 2.5 As ................................................................... 4-15
28 The result of low-time pass filtering the cepstrum of the waveform in Figure 10,a - 0.999, width of cepstral filter - ±4.5 As ................................................................... 4-16
U.
29 The result of low-time pass filtering the cepstrum of the waveform in Figure 10, -,
a - 0.999, width of cepstral filter - ±9.5 s ...................................... 4-17
30 The result of low-time pass filtering the cepstrum of the waveform in Figure 15,a - 0.9985, width of cepstral filter - 2.5 ................................... 4-18
31 The result of low-time pass filtering the cepstrum of the waveform in Figure 15, - •a - 0.9985, width of cepstral filter - ±4.5 As ................................................................. 4-18
32 The result of low-time pass filtering the cepstrum of the waveform in Figure 15,a - 0.9985, width of cepstral filter - ±9.5 s ................................................................ . 4-19
33 The result of low-time pass filtering the cepstrum of the waveform in Figure 15,a 0.90.9985 ................................. 5................................................................. 4-19
34 The result of low-time pass filtering the cepstrum of the waveform in Figure 15,a - 0.9980 ........................................................................................................................... 4-20
35 The result of low-time pass filtering the cepstrum of the waveform in Figure 15,a - . .... .................................................................... ............................................ ... 4-20
36 A typical large-angle Pentel lead-break waveform; the angle between the leadand the surface is 65................................... ...................................................................... 4-21
37 A typical small-angle Pentel lead-break waveform; the angle between the leadand the surface is 400 ........................................................................................................ .4-21
38 A Pentel lead-break waveform with secondary Pentel tip impact at a large angle ......... 4-22
39 A 200-point sample of a fixture-generated lead-break waveformnear the initial im pulse ...................................................................................................... 4-22
40 A 200-point sample of another fixture-generated lead-break waveformnear the initial im pulse ...................................................................................................... 4-23
vi
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.. .. . . -.- '
2L
LIST OF ILLUSTRATIONS (Cont'd)
Figure Page
41 Another 200-point sample of the waveform in Figure 39 near the later partof the w aveform ................................................................................................................. 4-23
42 Another 200-point sample of the waveform in Figure 40 near the later partof the w aveform ................................................................................................................. 4-24
43 The impulse response obtained by high-time pass filtering the cepstrum of the averageof 33 mechanically generated lead-break waveforms; a - 0.999 ................... 4-25
44 One of the 33 mechanically generated lead-break waveforms used in the averaging .... 4-26
45 The result of deconvolving the waveform in Figure 44 by the impulse response- in F igure 43 ........................................................................................................................ 4-27
46 An elliptical frequency filter used to reduce the high-frequency noise in the resultin Figure 45; -60 dB cut-off at 700 kHz ................................... 4-28
r 47 The result of filtering the waveform in Figure 45 with the elliptical filter in Figure 46 4-29
48 Relative amplitude of the stress corrosion events and the lead-break events .......... 4-29 •
49 Power spectrum of a stress-corrosion event captured by a resonance transducer ......... 4-30
50 The average of 31 stress-corrosion waveforms with their initial impulses lined upat the same location; the waveforms were captured with a resonance transducer ......... 4-31
51 The result of low-time pass filtering the cepstrum of the averaged waveformin Figure 50; no band-pass m apping ................................................................................. 4-32
52 The result of low-time pass filtering the cepstrum of the averagedwaveform in Figure 50; band-pass mapping between 100 and 300 kHz ......................... 4-33
". 53 Scatter plots of the first two principal components of the frequency componentsof two sets of events after low-time pass filtering in the cepstral domain .................... 4-34
54 Scatter plots of the first two principal components of the frequency componentsof the two sets of events in Figure 53 without filtering in the cepstral domain ............. 4-35
55 Scatter plots of the first two principal components of the frequency components56-of three sets of events after low-time pass filtering in the cepstral domain ................... 4-36
56 Scatter plots of the first two principal components of the frequency componentsof the three sets of events in Figure 55 without filtering in the cepstral domain ........ 4-37
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Section 1
INTRODUCTION AND SUMMARY
1.1 Introduction
Until recently, workers in the acoustic emission (AE) research community appearto have been unaware of a number of techniques applied successfully in other researchareas (including sonar, seismology, and speech processing) where certain advanced sig-nal processing techniques are frequently used to deal with distortion effects imposedon the signals of interest. For example, volume reverberation and multimode propaga-tion effects are common problems in these applications, and much effort has been ex-pended in the development of advanced techniques to compensate for them. Since 0these effects also severely distort real AE signals, those advanced techniques are ex-pected to be useful in improving the performance and reliability of AE-based nonde-structive evaluation (NDE) systems. This report describes the results of a research "program that seeks to capitalize on those successful research efforts, extending themand applying them to the problems of the detection, location, and characterization ofAE events.
1.2 Signal Processing
Current AE analysis techniques make limited use of the phase information in thereceived signal and rely on a variety of incoherent techniques for source identificationand location; pulse energies, rise times, ringdown times, and amplitude distributionsare commonly used signal parameters. Although these parameters often yield usefulinformation about the nature and location of the AE source, they do have serious lim-itations. In particular, they tend to be less useful when the signal-to-noise (S/N) ratiois poor, when complex structural features produce confusing reflections, or when mul-tiple sources are present. Unfortunately, the most important application areas for ,acoustic emissions often suffer badly from just these problems. Specifically, on-lineAE-based NDE systems often must deal simultaneously with adverse S/N ratios, com-plex structures producing serious multipath/multimode interference, as well as un-known (often multiple) source locations.
Coherent methods (which make use of the phase information) provide some basisfor hope in dealing with these complex problems. Unfortunately, linear methods tocompensate for these effects have not proven to be particularly useful. In light of therole of mode conversion and multimode propagation in signal distortion, this isperhaps not surprising. Nonlinear methods offer considerably more promise and, infact, have been used with much success in dealing with similar problems in other
fields. Homomorphic deconvolution especially has been used with considerable suc- .cess to eliminate multipath and multimode distortion in seismic, speech, and audioprocessing applications where S/N ratios are relatively good. A series of potentiallyuseful homomorphic signal processing approaches were developed under Phase I ofthis contract and are described in detail in the Phase I final report. This report willfocus on the experimental evaluation of the potential use these techniques may ulti-mately find in practical acoustic emission problems and, in particular, evaluate their
•1-.1- ..•.:
. .
"-.1
potential for compensating for transducer and structural resonances. Reliable mul-timode and multipath compensation, if achievable, can provide the technical basis forautomated on-line AE monitoring of complex structures for cracks; if the structural -
complexities can be reduced or eliminated, it may be practical to monitor crack growthrates, to carry out crack severity assessments, and to locate cracks.
In other situations, particularly when the S/N ratio is poor, homomorphicmethods, especially those based on cepstral techniques, are less useful and suffer fromproblems with accurate phase unwrapping. Under these conditions, adaptive nonlinearmethods may be very applicable. The experimental work reported here focused on the -deconvolution problem for situations where a relatively good S/N ratio was available.
1.3 Sensor Evaluation
The most commonly used AE transducers-resonant piezoelectric transducers-seriously distort the microstructure of AE signals through transducer ringdown.Although the nonlinear signal processing approaches outlined above will to a large ex-tent compensate for those problems, a better solution would be to use a transducerwithout massive intrinsic phase distortion. In this project we studied the performancesof both the resonant transducers and the conical transducers. The conical transducersused were commercially available piezoelectric sensors based on ideas developed and -demonstrated by Eitzen et al.' at the National Bureau of Standards. They have rela-tively flat frequency response up to 1 MHz. Such improved frequency response isachieved by reducing the contact area of the active element, by creating a smoothacoustical impedance transition to the backing material, and by increasing the backingmaterial volume. Because of the reduced contact area, however, the detected signalsare much reduced in amplitude compared to the resonant transducers, and very poorS/N ratios can be a serious problem in practical experimental situations.
1.4 Experimental Confirmation
Finally, as the major element of the Phase II contract effort, a series of experi-ments of gradually increasing complexity were planned and performed to confirm and ,- --evaluate the effectiveness of the signal processing algorithms and techniques devel-
oped. The experiments were carried out by General Electric at the Research andDevelopment Center and at the Materials and Processes Laboratory, in Schenectady,N.Y., under the joint direction of the co-investigators.
1.5 Summary.-
This project represents a radically new approach to the acquisition and analysis ofAE signals. The approach is based on the use of new signal processing methods andsensors and focuses on the removal of multipath and multimode distortion from the . ".
signals.
1-2
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Section 2
THE THEORY REVISITED
The analytical basis for this work is described in detail in the Phase I final report, ii:ili'.]and will not be repeated here. It should be noted, however, that in the course of car-
rying out the experimental portion of Phase II, it was discovered that some of thetheoretical results developed in Phase I of this project needed to be extended, and, insome instances, modified. Some of these changes came about in the course of analyz-ing the experimental data and in learning more about actual experimental uncertain-
ties. Other changes arose out of a more careful examination of the physical assump-tions behind the application of these techniques to the AE problem. The topicsmodified or added include exponential weighting, bandpass mapping, and the properchoice of the time distribution function in analyzing the multiple-event waveforms. . SDetailed descriptions of these changes, and the reasons behind them, are outlinedbelow.
2.1 Generalized Time Distribution Function for Multiple-Event Waveforms
As was shown in the Phase I report, the measured signals y(t) in acoustic emissionexperiments can be written in the form
y(t) - I ahp(t-Ti) h(t) g()+n(t) () -
where _J.* = the operation of convolution
h,(t)= the ringdown impulse response due to the boundary reverberationand the transducer response
hmq(t-r ) = the AE impulse pulse emitted at the source at time r,
g(t) = the measurement time gaten () = the background
The duration of the measurement time gate g(t) is assumed to be much longer thanthose of hp, and hr and therefore will be omitted from the rest of this report. Thispoint will be treated in more detail is Section 4.2, I.
2.2 Single-Event ApproximationSingle events represent a much simpler case, and in the case of a solitary event,
Equation 1 reduces to
y(t) - hpi(t) * h,(t)+ n(t) (2)
If the noise component n(t) is negligible, Equation 2 can be treated by the conven- ..-
tional homomorphic deconvolution technique to recover the signal hp,(t). Under thisapproach, the measurement y(t) is transformed to cepstral domain by thehomomorphic operation IFT(LOG(FT(y(t)))). This composite operation converts theconvolution operation into the addition operation. The cepstrum of y(t) is the sum of -
2-1
those of hp,(t) and h,(W, and hence the two cepstra can be separated by linear filter-ing.
This technique will work especially well when the cepstra of hp,(t) and hr (t) arewell separated in cepstral period. In AE measurements, these conditions typically aremet; typical AE hpis are narrow impulses with durations on the order of a few mi-croseconds, while the hrs have substantial low-frequency energy components and aremuch longer in duration. Since the cepstrum of a delta-like function is also a delta-like -function, the cepstra of the hpis are concentrated near the origin in the cepstraldomain.2 3 In general the cepstrum of h, is more spread out; so the criterion of separa-bility of cepstra is approximately satisfied. One way to further reduce the contributionof the cepstrum of hr near the origin is to convert hr into a minimum-phase sequenceby using the technique of exponential weighting, which will be described in detail inSection 2.4.
Once the cepstra of hp,(t) and hrt) are separated, they can be operated on by theinverse homomorphic transform to yield either hpi(t) and h,(t), respectively. Therecovered pulse shape hpi(t) can be analyzed for features associated with the particularclass of events characterizing the source. i2.3 Multiple Events " I
In general, AE events do not occur singly, but rather in associated bursts; in some : 1structures, the events may be easily visible as single pulses, but in large reverberantstructures, the individual pulses, extended by reverberation, will overlap and bedifficult to distinguish from one another.
2.3.1 Multiple Events with Occasional Single Events
On the other hand, provided that the AE events are associated with a localized .- .'crack formation and are statistically stationary, and further provided that a single re-verberated AE waveform is available for analysis, the derived ringdown function hr&t) - -
can be used to dereverberate the multiple-event waveforms (if they occur) from the • -
same source, through simple Fourier inversion. These dereverberated waveformswould reveal the original impulse time sequence of the overlapping individual events,and hence similar data from another transducer located at a different spatial location -.could be analyzed jointly via cross-correlation techniques to yield information on thetime of arrival and hence location of the events. Similarly, the rate of occurrence ofthese waveforms could be easily determined and could be used in estimating the ac- -
tivity strength and otherwise characterizing the source.
2.3.2 Overlapping Multiple Events
More generally, in dealing with multiple-event waveforms, one has to resort toEquation 1. Compared to Equation 2, Equation 1 has two complications: the constancyof the impulse shape hpi and the time distribution of the events. Assuming thedifferent events all have the common pulse shape hp () and only differ in their ampli-tudes a,, then we have
y(t) - hp) * p(t) * hWr(t)+n(t) (3)
where h.(t) is the AE pulse emitted at time t, and p(t) - Ta(i)8(t-7,) is the time2-2 . -
2-2"".,
7, - -'- a:a
, " .-.,.-
distribution of the events weighted with amplitudes corresponding to those of thedifferent events.
The cepstrum of the measured signal y(t) is then the sum of the cepstra of h,(t), p(t), and h(t). If the pulse train p(t) has been converted to minimum phase, it canbeen shown that its cepstrum is nonzero only for positive times greater than or equalto the interval between the first two arrivals,2 and thus is well separated from that ofhp(t) if the intervals between the impulses are not too close to each other. In thiscase, hp (t) can again be recovered by homomorphic deconvolution.
(If the different events do not have the same pulse shape, the signals,ajhpj,(t-r,) contained in the measurement y(t) cannot be simplified to a convolu-
tion of the pulse train p(t) with a common pulse shape h,,(t), as in Equation 3. Sinceit is difficult to estimate the cepstra of such complex signals, cepstral analysis is notpractical.) .
On the other hand, since the cepstra of hr(t) and p(t) usually overlap, h,(t) can-not be separated out. (Note that this result is distinctly different from the result re-ported in the Phase I study, where the assumption that an exponential distributionfunction holds for an ensemble of overlapping AE pulses lead to a contrary conclu- -
sion. A more careful analysis of the physical situation suggests that an exponential dis- 0tribution is not appropriate for an overlapping ensemble of AE pulses.) Fortunatelythere is another way out of this dilemma. The method works on the fact that if p(t) is .. "in fact a delta-like function, then the cepstrum of p(t) is also a delta-like function andthus is well separated from that of hr(t). One way to simulate this situation is byaveraging a large number of waveforms with one of the events in each waveformaligned at about the same location. A simple and practical way of accomplishing this,for example, is to use a transient waveform capturing device set to trigger on a strongimpulse. This will result in a series of captured waveforms where the first strong eventin each waveform which exceeds the triggering level always occurs at about the samelocation to in the waveform records. Under these circumstances, the time distributionfunction can be approximated by
p(t) - 8(t- to) + b (4)
where b represents the averaged time distribution of the other events in thewaveforms.
The procedure is illustrated in Figure 1. If the number of waveforms N used in the .averaging is large enough, b will approach a uniformly flat distribution. The magnitudeof b decreases with the number N, approaching zero as N tends to infinity. In thiscase pt) is basically a delta function with a cepstrum concentrated at the origin, andthus will not interfere with the cepstrum of h, (t).
Note that if there were no aligning in the averaging, all the impulses would be dis- - .tributed randomly in location, and p(t) would approach a uniformly flat distribution.Since the convolution of a flat distribution with any function is also a flat distribution,the averaged waveform y(t) is also a flat distribution and therefore contains no infor-mation at all.
2-3
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t
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Figure 1. The delta-shaped time distribution function obtained by averaging thetime distribution function of a large number of multiple-event waveformswith one of the events in each waveform aligned
2.4 Exponential Weighting
One of the steps in cepstral analysis is phase unwrapping, which is the process of" . making the phase 0 of the Fourier transform, r exp (iO), of the time series waveform
,." (a(n)) into a continuous function.2 However, if some Fourier components are zero,
- . their phase 0 would be undefined, and phase unwrapping would fail. This problem is-.. especially serious with waveforms of long record length. The reason for this is that
long record length corresponds to fine sampling in the Fourier domain, 4 and hencewaveforms with long record length are more likely to pick up zero Fourier com-ponents than those with short record length. This phenomenon is illustrated in Fig-ure 2.
Now the Fourier transform of a waveform corresponds to the z-transform of thefunction at the unit circle Iz= 1, where the --transform A(z) of a sequence a(n) isdefined as:
A (z) = a(n)z",
where z is a complex variable. ,
1J
2-4
-71.. .- °. . . ..- ....: -..: ..:. :....:.:..-. ...- ..- ,. ... .... .- ,-,-: -.,: .: ... ,.. -.. ..... :. :...... .- .. .,. ,. ..., -. -.. :.2":!
0
FT
TIME FREQUENCY
FT
TIME FREQUENCY
Figure 2. The relation between record length and frequency sampling interval
One way to get around the phase wrapping problem when some Fourier corn-ponents are zero is by using exponential weighting. 2 The original waveform (a 00) isweighted with the series (a") before z-transformation:
(a (n) - (a - °.% -
where a is a real number less than 1. Exponentially weighting a function by fa") hasthe effect of scaling the magnitude of the zeroes of the z-transform of the function by .-
a, as illustrated in Figure 3. Thus the zeroes in the Fourier transform of a functioncan be removed by exponentially weighting the function before inputting to thehomomorphic system, and phase unwrapping can be successfully carried out.
The use of exponential weighting can also improve the separability of the cepstra.If a is small enough so that all the zeroes of the reverberation sequence are scaled to -
lie within the unit circle, the sequence is converted to a minimum-phase sequence.Under this condition the reverberation sequence will contribute to the cepstrumn onlyfor positive times greater than or equal to the interval between the first two arrivals inthe sequence, 2 and hence the separability of the cepstra will be improved. In contrast,the structure of the cepstrumn of a mixed-phase sequence is complicated, difficult topredict, and frequently unstable.
Note that exponential weighting is different from the usual windowing procedure :*c
used in Fourier transformation, which is an approximation as far as convolution isconcerned. In general, convolution is not conserved under multiplication by a win-dowing function: the product of a windowing function, w(n), with the convolution of
2-5
. . -.... . . . . .
x(n) TIME SERIES
REAL NUMBER
x~)EXPONENTIAL WEIGHTING Xn
Yt X
Y2
Z=0 z SPACE
IZ 1, UNIT CIRCLE dFOURIER TRANSFORMATION
X1, X2 ZEROES OF z TRANSFORM OF x(n)
Y1. Y2 ZEROES OF z TRANSFORM OF a' x(n)
lyii = a X1 "
Y21 = .X
Figure 3. Removing zeroes in z-transform by exponential weighting
two functions, f(n) and g(n), is different from the convolution of w(n)f(n) andw (n) g(n):
w(n)(f (n) g(n)J fw(n)f (n)J (w(n)g(n)J
Convolution will be conserved, however, if W(n) is in the form a":.. -
a'(f (n) g(n)J (af f(n)] (an g(n)j fi
The output from the inverse homomorphic system is deweighted by the sequencefl/a"). The modified homomorphic characteristic system including exponential weight-ing is illustrated in Figure 4.
Figure 4. Modified homomorphic characteristic system Including exponentialweighting
2-6
F-2.5 Bandpass Mapping
If the signals one wishes to analyze have intrinsic bandpass characteristics, as, forU example, the data taken with resonant transducers, homomorphic analysis cannot be
accomplished by means of full-band homojmorphic systems. In fact, the analysis can-not be performed on the unit circle of the z-plane, since then the logarithm would be-come unbounded in the frequency bands with zero energy. Neither can it be per-formed off the unit circle, since the z-transform of such signals does not convergeanywhere on the z-plane, but on the unit circle. Thus the exponential weighting pro-cedure used to remove the zeroes of a signal off the unit circle cannot be applied tothe class of bandpass signals. Since real data always contain some out-of-band noise,and can only have a countable number of zeroes on the unit circle, sometimes it ap-pears possible to employ the exponential weighting procedure to remove such zeroesfrom the unit circle. Such an approach, however, is inherently ill-conditioned, andoften leads to erroneous results.
One way to solve this problem involves a restriction on the domain of the logarith-mic mapping to encompass only the passband of the input. This approach may be con-veniently formulated in terms of a frequency scaling operation that shifts and stretchesthe signal's passband to occupy the entire frequency domain, as illustrated in Figure 5.The result of this operation is then a full-band sequence, which may be analyzed usingfull-band homomorphic systems. The analyzed output from the homomorphic systemundergoes the inverse bandpass mapping, The characteristic system for bandpasshomomorphic systems is illustrated in Figure 6.
--
/ / FREQUENCY
/ SHIFTING & INTERPOLATION
i: /\.--"
L(
FREQUENCY
Figure 5. Bandpass mapping operation
2-7
S.,.:..::._ _
BP. • Lo .. "--1n 1n Z- ';'n"
Figure 6. Characteristic system for bandpass homomorphic systems
Bear in mind that bandpass mapping is not a panacea, but rather a method to re-move the effects of the out-of-band noise in phase unwrapping. It does not add any in- -
formation in the frequency bands with zero energy and may not produce particularlysatisfying results, especially if the system under analysis is sharply resonant, with a rel-atively small range of useful, information-carrying frequencies.
2-8
. . . . .
. . . . .-.. -... ... .... .-- ...- ..-. --........ .
- -.. -- . - - . r. 0" " . "
Section 3
EXPERIMENTAL APPARATUS
A VAX-based experimental system was assembled to provide a suitable testbed forthe acoustic emission experiments carried out under this contract. The system, shownin schematic form in Figure 7, provided a great deal of flexibility in the acquisition,validation, and analysis of the acoustic emission data. Data acquisition, for example,was carried out under VAX control; this approach gave the experimenters access toVAX-based tools to monitor the newly acquired data and verify its integrity during thecourse of the experiments. In addition, the VAX system incorporated an interactivedigital signal processing software system, which was used extensively in the analysis ofthe data; the system was useful not only in the exploratory stages while appropriate al-gorithms were being developed, but also during the production analysis phase when •validated experimental data were being batch processed. Subsequent sections of thisreport will provide details on the hardware and software used in these experiments.
~-54 cm -.. ~.TEST PLATE PENTEL EXCITATION I
TRANSDUCER 1 TRANSDUCER 2
PREFILTER PR FILTER
10kHz- 1 MHz 10 kHz- MHz
AMPLIFIER AMPLIFIER!.-
20 k z 1 M z 20 kHz I MHz ;li..2il ?
BIOMATION 8100
TRANSI ENT RECORDER•
FIGURE 8 - BLOCK DIAGRAM OF THE DATA ACQUISITION SYSTEM.
Figure 7. Block diagram of the data acquisistlon system
3-1
At
3.1 Hardware
The hardware used in the acoustic emission experiments will be described in thesubsequent sections essentially in the same order as the signal flow through the sys-tern. Figure 8 shows the experimental setup; the thick test plate can clearly be seen, ascan the transducers, the Biomation transient recorders, the analog instrumentation,and the VAX 11/750 control/analysis computer in the background.
Figure 8. The experimental setup, showing the thick test plate, the Biomationtransient recorders, the analog Instrumentation, and VAX 11/750control/analysis computer
3.1.1 Specimens
A series of experimental specimens was prepared to provide a reasonable range ofexpected reverberation conditions; a key element in the design was the notion that itshould be possible to increase gradually, and in a controlled manner, the physical corn-plexity of the experiments, so that new conditions were added one at a time.3.1.1.1 Workpieces. Two aluminum plates were selected to conduct the experiments.The first one was a relatively thick plate with dimensions of 27 x 5 x 2 in. The thickplate was chosen to allow clean near-field measurements withdut the confusing effectsof reverberations from the back wall and other reflections. It functions in a near-fieldsense as an infinite half-sphere, and has known solutions for the expected AE due to aPentel pencil lead break. The first plate is set up on a 2 in. thick foam pad to isolate
3-2
i-
from ambient vibrations. The second plate had dimensions of 27 x 25 x 1/4 in. andwas chosen to allow the investigation of the effects of plate bending vibrations andnear-field resonance, as well as edge reflections. Only the thick plate was used formost of the experiments described in this report... .
3.1.1.2 C-Block Stress Corrosion AE Sources. Notched aluminum C-blocks, undertensile stress and subject to a corrosive solution, were used to generate natural acous-tic emissions. The notched C-blocks were clamped to the test plate and coupled withglycerine, so that good transmission of the generated AE pulses was achieved. A sodi- --
um chloride solution was subsequently used to induce stress corrosion cracking in the..notched block. These sources provided reliable, natural AE signals, and could be easilycontrolled by small adjustments in the stress and/or salt solution so as to provide awide range of natural AE signals, ranging from weak, individual pulses to nearly con-tinuous trains of strong pulses.
3.1.2 Transducers
Both conventional resonant transducers (Physical Acoustics Corporation, ModelPAC R15) as well as conical low-resonance wide-band transducers (Industrial QualityInc., Gaithersburg, Md.) were used to detect the acoustic events. The resonant trans-ducers have a band frequency response between 100 and 300 kHz. The conical trans- -ducers have a flat frequency response up to 1 MHz.
3.1.3 Analog Signal Conditioning Equipment
The signals from the transducers were first amplified using a Tektronix Model 502amplifier with internal low-pass filter set at 1 MHz, or lower, depending on the nature
of the sensing transducer. These signals were further processed using a Kronhite pro-grammable filter (48 dB/octave/section) set up to low pass below 1 MHz. The outputof the filter was then connected to the Biomation transient recorder system. A Nicoletdigital Explorer scope was used for a visual display of the signals prior to transmittingthem into the computer.
3.1.4 Transient Waveform Recorders
Biomation 8100 digital transient recorders were used to record and sample theacoustic emission signals. Using a single Biomation 8100, 2048 samples can be ob-tained in single-channel mode; in dual-channel mode, two parallel channels of 1024 Ssamples can be obtained. The recorder operates at up to a maximum sampling rate of100 MHz, if desired. For single-channel operation, a 2 MHz sampling rate results inthe acquisition of nearly 1 ms of data. Longer records needed to verify the Phase I re-suits were obtained by ganging together four of these systems in series. Using this ar-rangement, nearly 4 ms of continuous data could be acquired from a single AE event, •_if required. A VAX-Biomation interface board was designed and fabricated to provide
both automated experiment control by the VAX, as well as a data path for thetransmission of transducer signals from the Biomnation recorder into the DEC VAX11/750 computer for later postprocessing. The hardware and software for this data ac-quisition system were designed and put together during the duration of this contractspecifically for these AE experiments.
3-3
S - . *
3.1.5 Stress-Corrosion Event Monitor
A conventional AE transducer, in conjunction with a Dunegan/Endevco 920 Distri-bution Analyzer and a Tektronix 604 Monitor, was used to monitor the rate of arrival a ,and the intensity of the stress-corrosion events. This information allowed us tocategorize easily the state of the C-block stress corrosion AE source, as well as provid-ing a useful reference standard against which to measure the new analy'sis methodsunder evaluation.
3.2 Software
A variety of software modules were employed or developed to serve the needs ofthe experimental effort. Software modules were developed or used for data acquisi-tion, data validation, algorithm identification, homomorphic data analysis, feature ex-traction, and pattern recognition. Much of the data analysis was carried out using aninteractive, interpretive, high-level digital signal processing language available fromSignal Technology Inc. (Santa Barbara, Calif.) called ILS. "Recipes," consisting ofDEC DCL command procedures interpretable by ILS, are provided for all the analysiscarried out using ILS. In some cases, where ILS did not provide appropriate functionalmodules, new ILS procedures were developed to provide the needed functionality. Ineitbhr case, the modules used will be functionally described below; source code, anddocumentation for those developed under this c, .tract, can be found in the appen-dices.
3.2.1 Data Acquisition
Software was developed to interface the Biomation hardware with the VAX 11/750computer and to provide some measure of validation for the experimental data. Addi-tional software was developed to prepare the input data in a form compatible with thehigh-level signal processing language (ILS) which contains a variety of softwaremodules for data analysis.
3.2.1.1 VAX-Biomation Interface. A data acquisition/control software system was puttogether to acquire data with, and control up to, four Biomation 8100 transient record-ers with a VAX 11/750. The Biomation interface software is MACRO-based and con-trols a DR-i1C parallel interface board. The interface permits VAX-based softwarecontrol of the Biomation recorders. All of the Biomation front panel switches and con-trols can be set via software commands originating in the VAX. In use, the Biomationtransient recorders are operated in parallel, with one of the recorders providing trigger- -
ing synchronization signals for the others. The trigger delays were set so that the cap-tured data records would overlap slightly. The captured data records were processed bya VAX FORTRAN program that carried out correlation calculations on the overlappedregions to verify that the record segments were correctly synchronized, making ap-propriate corrections if required. In addition, the overlapped regions were used to ad-just the gain and offset on each record to compensate for record-to-record variations.Finally, graphics software permitted the experimenter to view the captured records, orany subset of them, prior to proceeding. Complete documentation on the system, in-cluding functional descriptions, schematics, and software listings can be found inAppendix A.
3-4
~~~~~~.'.. . . .. .. .... .................-.... ..... .. ...................... .•... %
3.2.2 AnalysisThe basic approach in developing analysis software was to carry out as much of the
analysis as possible directly in the ILS (see Appendix B) digital signal processing -
language; ILS is an expressive language, licensed by Signal Technology Incorporated,and provides a flexible ensemble of digital signal processing primitives built into its .'-
structure. In addition, ILS provides many kinds of generalized support functions, in-cluding data editing capability, simulation software, graphics software, and extensivepattern recognition software. ILS graphics capability, for example, supports graphicsprimitives for either interactive or hardcopy display, along with the associated support "functionality.
Many complex functions can be constructed by stringing together primitive func-tional modules into DCL command procedure recipes. These recipes are executable ei- _ -
ther on a stand-alone basis, or as new primitive modules in more complex primitives.All the recipes used in analyzing the data in this report are included, where appropri-ate, with the figures in Section 4 displaying processed data. Finally, it is relatively easyto add entirely new modules to the ILS system.
Perhaps the most important feature of ILS is that it is intended to be used bynonprogrammers; thus it allows a researcher familiar with digital signal processingtechniques to explore new techniques very quickly. This approach allowed considerableflexibility, and proved to be a very effective way to analyze and process quickly theacoustic emission data acquired under this contract.
3.2.2.1 Homomorphic Analysis. A software package was developed under Phase I atRensselaer Polytechnic Institute to carry out simulation studies on the application ofhomomorphic analysis to acoustic emission signals. This package was based on theroutines published in the IEEE volume Programs for Digital Signal Processing Aftersome changes and modifications, the package was installed in the VAX computer sys-tem and integrated with the ILS digital signal processing package as the XCP module.Besides altering the code to conform to the ILS functional conventions, two basicchanges were made to the existing code. The first change consisted of adding variableexponent exponential weighting capability to convert the acquired waveforms to . .,minimum phase sequences, which are analytically more stable than mixed phase se-quences. (See Section 2.4 for a description of the theory behind exponential weight-ing.) The second change involved adding bandpass mapping, necessary to deal with thesignals produced by narrow-band resonant transducers. (See Section 2.5 for a descrip-tion of the theory behind bandpass mapping.) The source code and documentation forthe XCP ILS module can be found in Appendix B.
3.2.2.2 Feature Extraction and Pattern Recognition. A feature extraction and patternrecognition package was put together to investigate the separability of the differentgroups of waveforms. The package was based generally on the pattern recognitionsoftware available in ILS. Since the ILS pattern recognition modules were originallydesigned for speech and speaker recognition, minor changes had to be made to someof the modules to make them suitable for this application. The process followed in us-ing the pattern recognition package to analyze acoustic emission waveform data wasthe traditional training/test set approach. A set of waveforms is analyzed and used totrain the system; subsequent sets are tested against the training set for statistical com-patibility. Summarizing the process, each of the waveforms in the group is Fourier •transformed to extract a number of Fourier components. These Fourier components . -
3-5
. . . . . . . ...-.. .-.--.... . . .
are then processed to yield the mean waveform, the covariance matrix, the Fischerlinear discrimination matrix, and the eigenvalues and eigenvectors for each group ofwaveforms. Using these intermediate results, principal component analysis is carried -
out on sets of waveforms. In essence, principal component analysis projects the groupsof waveforms onto a discriminant plane with maximum separation between the -
groups. A scatter plot is then made using the first two principal components, and thestatistical properties of each of the groups can be computed. Finally, the mean separa-tion between groups can be expressed in statistical terms and used to characterize theprobability that a given test value is in fact a member of the training set. A completedescription of the software modifications to the ILS modules can be found in Appen-dix B.
3.Md?-'
• ...
L.- -
*~. " .i .. ,..dd .* * .~ ~ *j .- . ..
Section 4
EXPERIMENTAL RESULTS
The block diagram of the experimental layout, hardware, and associated electronicswas shown in Figure 7 of the previous section.
A problem encountered very early in the analysis was that our available methods - - ..
for recording and for carrying out analog- to-digital conversion of the data did not pro- .vide sufficiently long record lengths for our analysis. Initially, the data acquisition sys-tem utilized a single Biomation 8100 interface providing a pair of 1024-point-longrecords. For sampling rates of 10 MHz, this system provided records approximately0.1 ms in duration, insufficiently long for reverberations to decay in the experimentalfixtures we employed. Accordingly, several different hardware approaches for record-ing and analog-to-digital conversion were explored to try to identify a more suitable 0means of acquiring the large experimental data sets needed to confirm the results ofPhase I. The first approach explored was to reduce the sampling frequency to 2 MHzand to use the Biomation recorder in single-channel mode, so that a single 2048-pointrecord is obtained instead of a pair of 1024-point records. This technique yields arecord duration of roughly 1 ms, which-although still too short to record the entireringdown train-provided enough data to begin analysis.
Later the record length was increased fourfold to 8096 points by connecting fourBiomation recorders in series, as described above in Section 3.1.4. At a sampling rateof 2 MHz, this arrangement gives a record length of about 4 ms, which was adequatefor subsequent analysis.
The command procedures for generating the ILS plots shown in Figures 9 and fol-lowing are included in the illustrations. The DSP command at the end of most of theinstruction sets displays the result in sampled data form.
4.1 Calibration jil
The breakage of Pentel pencil leads was employed as a calibration source. In theinitial phase of the experiments, the 0.5 mm HB leads were broken manually.
Two typical lead-breaking waveforms are shown in Figures 9 and 10. They are twoseparate events taken with two of the wide-band, NBS-style conical transducers spacedabout 54 cm apart on the 27 x 5 x 2 in. aluminum block. Pentel lead breaks weregenerated relatively close to transducer 1 at the location indicated. Signals from trans-ducer 1 triggered the Biomation to accept data. The Biomation was set to the pretriggermode. The data were low-passed at 1 MHz with the Kronhite filter, sampled at 2 MHz,for a 2048-point record. The waveform shown in Figure 9 is the output from transduc-er 1, while the waveform shown in Figure 10 is from transducer 2.
The time difference between the two pulses in Figures 9 and 10 is about 200 As,which is reasonably close to the value of 176 /As calculated from the geometry of thesetup, assuming the shear wave speed in aluminum to be 3.1 km/s. The waveformsexhibit low-frequency ringdown due to the reflections in the aluminum block.
4-1
-----------
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Figure 9. A typical lead-break waveform recorded by an NBS conical transducer
. ALUES 5 7
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Cfl 2648PIL 5636 (IEASUSED WAVRPOIM WD FILE NO.)~jj DSP 1,1,2036
Figure 10. Another lead-break waveform recorded by an NBS conical transducer lo-Icated 54 cm from the one used in Figure 9
4-2k J
Homomorphic deconvolution was performed on the waveform in Figure 10. Thecepstrum of the waveform is shown in Figure 11. The result of passing the cepstrumthrough the low-time window w (t):
1 -9.5 As < t < 9.5 /As
w(t) = (5)I otherwise
and then inverse transforming is shown in Figure 12. An impulse type of function is 9recovered, but the result is not very clean: the ringing in the background is quite seri-ous.
A large improvement was brought about by employing the technique of exponen-tial weighting to minimize the effects of reverberation. The result of applying exponen-tial weighting to the waveform in Equation 10 with a = 0.9955 and using the low-time . .window given by Equation 5 is shown in Figure 13. The recovered signal is muchsharper and cleaner, and in fact compares favorably with the theoretical Pekaris solu-tion, which is shown in Figure 14.
'AL- E
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Pht 561 (1 IS ThE SECONDARY RD PIE 0IL NO., 4 1,9994,TO STORE THE CEPSTRUN)
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Figure 11. The cepstrum of the waveform in Figure 10
4-3
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Figure 12. The result in the time domain of low-time pass filtering the cepstrum ofthe waveform in Figure 10
4.2 Effect of Record Length
Another problem encountered was that the ringdown response of the mediumcould last substantially longer than the maximum record length, for as long, in fact, as :2several seconds under some circumstances. The record length of a waveform deter-mines the fraction of ringdown captured, and hence the amount of leakage error inthe Fourier transformation operation in homomorphic analysis. One would certainlyexpect the results to improve substantially when the record length is increased. As weshall see, however, if the effect of the record length is not significant enough, the im-provement brought about by longer record length could easily be masked by other -
sources of errors.
The effect of the record length is demonstrated in the results shown in the se-quence of Figures 15-26. Figures 15-18 are four lead-breaking waveforms capturedwith a conical transducer, the source being located at distances 45, 45, 30, and 15 cm, -respectively, from the transducer. The signals were low-pass filtered at 1 MHz, sam-pled at 2 MHz, and are 8096 points in length. Each of these waveforms wastransformed to the cepstral domain, then low-time filtered with the w(t):
1 -4.5 /As < t < 4.5 jus. -].
W) W (6)
otherwise .. ,
4-4
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Figure 13. The improved result obtained through the use of exponential weighting;a=0.9955
and finally inverse- transformed to the time domain. The value of a used in exponen-tial weighting is 0.9985. Figures 19 through 22 show the results obtained in this wayusing all of the 8096 samples of the input waveforms in Figures 15 through 18. Incomparison, the results obtained using only the first 2048 samples of the inputwaveforms are shown in Figures 23 through 26. Identical values of a and w(t) areused in both cases. In comparing the two sets of results, although Figure 19 is muchcleaner than Figure 23, the improvement caused by the longer record length is lessobvious in the other three cases. From these results it may be concluded that the leak-age error in Fourier transformation in going from 4.096 ms (corresponding to 8192
* points at 2 MHz sampling rate) to 1.024 ms is not significant compared to the othersources of errors in the experiments and analysis. The lack of improvement withlonger record length may also be due partially to some transient instabilities in the gainand noise characteristics of the four Biomnation recorders. At any rate, the recordlength of 1.024 ms provided by one Biomnation recorder at a sampling rate of 2 MHzappeared to be long enough for our purpose. The waveforms used in some of our lateranalyses were 1.024 ms in length.
I4-5
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Figure 14. The theoretical seismic surface pulse according to Pekaris
4.3 Dependence on the Width of the Cepstral Filter-
The ideal width of the cepstral filter used to separate out the signal impulses fromthe recorded waveforms was determined empirically. The results indicated that in mostcases a filter centered around the origin in the cepstral domain with a width of about4.5 As worked best. Two typical sets of results are illustrated in Figures 27-32. Figures27-29 show the results of low-passing the cepstrum of the recorded waveform in Fig-ure 10 using a - 0.999 in exponential weighting and cepstral filters of widths ±t 2.5,± 4.5, and :±9.5 ls, respectively. Figures 30-32 are the results of applying the same
* . procedure to the waveform in Figure 15 using a = 0.9985 in exponential weighting. Inboth cases, the cepstral filter with a width of ±4.5 /As yielded the best results.
4.4 Dependence on Alpha
In the homomorphic analysis of single-event waveforms, exponential weightingconverts the original time sequences hp (i) and hr(fl) to the new ones a~ h,(n) anda'hr(n). The value of a determines the distributions of the cepstra of the two ex-ponentially weighted time sequences, and hence the results of the homomorphicdeconvolution depend on the value of a used in the exponential weighting. To studythe extent of this dependence, homomorphic analysis was performed on the waveform.
* in Figure 15 with the window w(t) in Equation 6 but with different values of a, in the
4-6
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Figure 15. A lead-break waveform recorded by an NBS conical transducer located45 cm from the source
-RLUJES
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Figure 16. A lead-break waveform recorded by an NBS conical transducer located45 cm from the source
4-7
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Figure 19. The result of low-time pass filtering the cepstrum of the waveformin Figure 15, using all of the 8096 samples as input; a - 0.9985
exponential weighting. The results corresponding to a - 0.9985, 0.998, and 0.9975 areshown in Figures 33, 34, and 35, respectively. The results indicate that even a slightchange in the value of a affects the results significantly.
4.5 Fourier Deconvolution
Initial efforts to use the transfer function obtained in the homomorphic deconvolu-tion of one Pentel lead-breaking waveform to deconvolve other Pentel lead-breakingwaveforms were met with little success. To understand the difficulties, the repeatability
of the manually performed lead-breaking waveforms was examined in detail. It wasfound that the lead-breaking signals depend critically on (1) the precise angle the leadmakes with the surface and (2) possible secondary Pentel tip impact after the lead -break.
These findings were illustrated in Figures 36-38, which are manually performedlead-breaking waveforms captured with a conical transducer. Figures 36 and 37 illus-trate the dependence of the signal on the angle between the lead and the surface. Thewaveform in Figure 36 was generated with an angle of about 650, and the one in Fig-ure 37 with an angle of about 40° . The waveforms are markedly different. It appears
4-9
VALUES32766
-82768
-62760 I I I
ME 0 .6 SEC MID 5S.12E-04 SEC END0 .0010.4 IEL
REPLACE 0166 By 646@ IN THE RECIPE FOR FIG. 19
Figure 20. The result of low-time pass filtering the cepstrum of the waveformin Figure 16, using all of the 8096 samples as input; a - 0.9985
-7 ft
.* VRLUES
* 327668
16384
w. .63 1
-32768 I I I I I I Ir BEG 0.0 SEC MID .4.E-84 SEC E 1 . 4 . tE,
REPLACE $610 BY 860 IN THE RECP FOR FIG. 19
Figure 22. The result of low-time pass filtering the cepstrum of the waveform
in Figure 18, using all of the 8096 samples as input; a 0.9985
that the angle determines the amount of shear and transverse waves generated in eachevent. A shallow-angle (<450) event contains relatively more low-frequency com-ponents and is relatively featureless. On the other hand, a steep angle (-60-70)produces strongly featured signals with much modulation. A Pentel lead break withsecondary Pentel tip impact at large angle is shown in Figure 38. The secondary impactgenerated additional AE activity in the midregion of the waveform.
In an effort to produce repeatable lead-breaking signals, a fixture for breaking leadsin a well-controlled manner was acquired. The fixture allowed precise control over theangle of the lead during breakage and effectively eliminated problems with periodicsecondary tip contact. Further studies on the feasibility of Fourier deconvolution werecarried out using waveforms generated with the help of the fixture. It was found thatthe waveforms were highly repeatable. The repeatability is demonstrated in Figures 39and 40, where 200 points of two such waveforms are shown near the initial impulses.These waveforms were recorded by a conical transducer and sampled at 2 MHz. Fig-ures 41 and 42 show another 200 points in the later part of the two waveforms. Minor
r-" differences between the two waveforms are visible after a considerable delay, but theoverall similarity is still very impressive.
Fourier deconvolution using these mechanically generated waveforms yielded en-rcouraging results. Figure 43 shows the impulse response obtained by the following .- .,-: procedure: .
o Averaging 33 of such waveforms (Pentel lead breaking by a mechanical devicerecorded by a conical transducer), each of the waveforms being 1024 points in
length
4-11
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'ALUES
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BEE 0.6 ,EC YIO -. 1-E 0~4 E,. 4 124S L':
PFIL 81913 (MEASURED WAVEFORM NO FILE NO.)rIL SOClHS_,2948 (Ni IS THE SECONDARY WD FILE NO0., @ NI19996,
TO STORE THE FIRST 2 648 CHANNELS or FILE B160)
HOF $6,63,-32999TSP HTSP 1,1,1,196 (COPY THE FIRST 246 CHANNELS or FILE Sig@
TO P ILE N05I
PL SOS (02 IS THE SECONDARY NOD FILE NO.. OIN2,999•.
TO STORE THE CEPSTRUM)
SXCP, B (EE TH E DESCIPTION 1 FIG. Ili
.1..
FXCPLOV (SEE THE DESCRIPTION IN FIG. 12)
':2>C3 (N3 IS THE SECONDARY WD FILE NO., @<N3<9998,
To STORE THE INVERSE CEPSTRUN)
'11%
2649
;2540DSP S.131H96
3Figure 23. The result of low-time pass filtering the cepstrum of the waveformin Figure 15, using only the first 2048 samples as input; a 0.9985
*Calculating the cepstrum of the averaged waveform, ar 0.999High-pass filtering the cepstrum, i.e., setting the low-time portion of the cep-strum to zero for I < 4.5 us
*inverse-transforming the cepstrum to the time domain
The result of deconvolving one of the 33 waveforms used in averaging, the onetshown in Figure 44, by the impulse response in Figure 43 is illustrated in Figure 45.
The result was improved by removing the high-frequency noise with the elliptical fre-quency filter shown in Figure 46 with -60 dB cut-off at 700 kHz; the filtered result isshow in Figure 47.
The deconvolution results shown in Figures 45 and 47 were obtained under closeto ideal conditions:
*Obtaining highly repeatable waveforms by breaking Pentel leads with a mechani-cal device
4-12
KIL N
-. S2 2 ISTH.ECNDRY.r F.EN..i- h2.98,"'.
VALUES
32768
16384
S .
-16384
-32'68 I I I -
BEG 0.6 SEC MIO . L. -6 E " .
RIPLACI 0100 BY 54#l IN THE RECIPE FOR FIG. 23
Figure 24. The result of low-time pass filtering the cepstrum of the waveform "--in Figure 16, using only the first 2048 samples as input; a - 0.9985
VALUES3276"""
" ""
16384
-163a4
4--f
• .
* 32768 - -------- ! . .. ----.
BEG 0 .6 SEC MID S.I.E 04 IR.: N, .00V1'
REPLACe S1l0 By eSIe IS THE RECIPE tOR PIG. 23
Figure 25. The result of low-time pass filtering the cepstrum of the waveformIn Figure 17, using only the first 2048 samples as input; a - 0.9985
4-13
-- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ - - -. ** ;...:'- .:*:~:~ .:~*~: - . .'_.'. , " . . . . . . -. . . , , . . . . - , . . . . . . . . . .. .. .-.,
3276a
16384 -3278
- 4i-.-' -- --
BEG 0.6 SEC MID Y.12E-8M 4 E t1
REPLACE 816 BY 866 IN THE RECIPE FOR FIG. 23
Figure 26. The result of low-time pass filtering the cepstrum of the waveformin Figure 18, using only the first 2048 samples as input; a =0.9985
0 Recording the waveforms with a wide-band conical transducer
Using a relatively short record of 1024 points, where the similarity betweenwaveforms is extremely good
In Figures 45 and 47, the presence of the impulse is obvious, yet the quality of thepulse shape does not appear to be good enough for identification purposes, even afterlow-pass filtering to remove high-frequency noise. These results indicate that Fourier '
deconvolution is too sensitive to the minor differences in the recorded waveforms tobe of any value for event identification in practical situations.
4.6 Effects of a Limited- Frequency Band
Realistic acoustic emission events were generated using aluminum C-blocks subjectto stress and a salt solution. It was found that the amplitude of stress-corrosion eventsgenerated in this way was about 60 dB lower than the amplitude from Pentel leadbreaks; this finding can be seen clearly in the amplitude plot shown in Figure 48. Un- -jfortunately, since the sensitivities of the conical transducers are much lower thanthose of the resonant transducers, the stress-corrosion signals could not be detected bythe conical transducers at all. For this reason, resonance transducers were used fordetection.
The data taken with the resonance transducers are band-limited between 100 kHzand 300 kHz. The power spectrum of one of the stress-corrosion waveforms capturedwith a resonance transducer is shown in Figure 49. As mentioned in Section 2.5. suchdata require bandpass mapping to suppress the effects of noise propagation in the
4-14
............. .................................... .. "''
3278
16384 -
- 16384
-32768 L
BEV 0.0 SEC MID 5.1 E -- E, .U2.
PhL 500 (MEASURED WAVEPORN 15FILE NO.,P~IL 5111 fNI IS THE SECONDARY WD FILE No., 'S'NR
TO STORE THE CEPSTRUM)XC?.I . (SEE THE DESCRIPTION IN PIG. 131
OCILOW (SEE THE DESCRIPTION IN FIG. 12)
'2 (72 IS THE SECONDARY FILE NO., 0,142..NO0,TO STORE TH E INVERSE CEPSTRUM)
-6.2044US
Figure 27. The result of low-time pass filtering the cepstrum of the waveformin Figure 10, a =0.999, width of cepstral filter :t±2.5 /is
unoccupied frequency band in the process of phase unwrapping. Figure 50 shows theaverage of 31 stress-corrosion waveforms with their initial impulses lined up at the
* same location, as mentioned in Section 2.3.2. The waveforms were captured with a* resonance transducer, were sampled at 2 MHz, and were 2048 points in length. The
result of low-pass filtering the cepstrum of the averaged waveform without bandpassmapping is shown in Figure 51. The value of a used in exponential weighting is 0.999,
* and the low-time cepstral filter w(l) is given by
1~)=j -4.5 ;As < n < 4 .5 Mg
- 0 otherwise
Figure 52 shows the improved result brought about by bandpass mapping between
100 kHz and 300 kHz. Even with bandpass mapping, there is still severe ringing andbroadening in the impulse signal caused by the lack of information in the frequencyband with zero energy.
4-15
-79
REPLACE .. . .PAAETR .AN-- 2.4 1-. . ..CIEFR I. 7B
3:763-
I I
SAC " . E:MD"51Ee E END .041424 $EC
1I AND 2046 RESPECTIVELY
Figure 28. The result of low-time pass filtering the cepstrum of the waveformin Figure 10, a = 0.999, width of cepstral filter = --4.5 As
Figure 51 indicates that the band-limited nature of the waveforms recorded usingresonance transducers gives rise to severe distortions in the impulses obtained by low-pass filtering the cepstrum of the averaged waveform in Figure 50. Bandpass mappingcleans up the result considerably by suppressing the error propagation in the unoccu-pied frequency regions, but severe ringing and broadening is still present as shown in -,
Figure 52. This ringing and broadening is due to intrinsic limitations of the band-limited nature oi the data-resulting from the use of resonance transducers-andtherefore cannot be removed by signal processing.
4.7 Pattern Recognition
The quality of the homomorphically deconvolved signals obtained above does notgive one much hope for accomplishing source identification. This observation wasconfirmed in the following pattern recognition analysis using two sets of waveformsfrom different sources, with nine waveforms in each set. In one set are waveformsgenerated by rubbing sandpaper on the edge of one end of the aluminum block, whilethe ones in the other set were generated by rubbing the sandpaper on the face of thesame end of the block. The waveforms were sampled at 2 MHz and are 2048 pointsin length. Each of the waveforms was homomorphically deconvolved to recover thelow-time component in the cepstral domain, using a weighting of 0.9985 and a cepstralcutoff time of ±4.5 As. These deconvolved signals were Fourier analyzed, and the 20Fourier coefficients from 976.56 Hz to 594.7 kHz at 31.25 kHz intervals were extract- -. --
ed. Principal component analysis was performed on these 20 Fourier coefficients of
4-16
:''': -., -'' .-' . .... ..: :....*.:.. .... ...........................- -.,-''.-..-:-.-'''.-. ' :''.---' ...'''= '-'.-:
VALUES32768
16384
-6. ,_______,_________:____
-32760II I-BEG 6.6 SEC MID -5.12E-0 SEC END .46164 E
REPLACE T" : PARAMETERS 6 AMD 2644 IN THE RECIPE FOR FIG. 27 BY26 AND 2826 RESPECTIVELY
Figure 29. The result of low-time pass filtering the cepstrum of the waveformin Figure 10, a =0.999, width of cepstral filter = E9.5 As
the two sets of 9 waveforms in each set using the software in the ILS signal analysisSpackage. The first two principal components are plotted in Figure 53. (See Appendix C
for a description on pattern recognition and examples of command procedures for Fig-* ures 53 and following.) The results in Figure 53 indicate the two sets of waveforms
cannot be distinguished from each other. In comparison, the first two principal com-* ponents of the raw data without cepstral filtering are plotted in Figure 54. The two sets
of waveforms become less separated after the cepstral filtering.
Similar results were obtained when the above procedure was repeated with an addi- -
tional set of nine lead-breaking waveforms. The plots of the first two principal corm-ponents with and without cepstral filtering are illustrated in Figures 55 and 56. Again,cepstral filtering failed to improve the separability of the three sets of waveforms.
L 4-17
VALUES32766-
4 £-63842
sea 0 .6 SEC MID - 5.12E-44 SE ENDJ .001024 SEC
REPLACE THE PARAMETERS 16 AND 8184 18 THE RECIPE POR PIG. 19 BY6 AND 808 RESPECTIVELY
Figure 30. The result of lowi-time pass filtering the cepstrum of the waveformin Figure 15, a =0.9985, width of cepstral filter = 1 ± 2.5 M~s
WRLUES
3268
-16964
BEG. . SE~C -110 3..1 -F C. 1 0. ~l4SAllE AS FIG. 19
Figure 31. The result of low-time pass filtering the cepstrum of the waveformin Figure 15, a - 0.9985, width of cepstral filter - ±4.5 M5
4-18
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-'ALLIES32768
* 163811
S 26 EG 0.4' ,EC MID - Y.12E-04 SEC END .0B01B2I SEC
REPLACZTgt PARAMETERS IS AND 8184 IN THEl RECIPE FOB FIG. 19 BySBAND 817 4 RESPECTIVELF
*Figure 32. The result of low-time pass filtering the cepstrum of the waveform
in Figure 15, a =0.9985, width of cepstral filter -t±9.5 /is
.ALLIES
32-6
a.
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Figure 33. The result of low-time pass filtering the cepstrum of the waveformIn Figure 15, a - 0.9985
L 4-19
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RUPLACS TE PARAMBTZR 6.996S IN THE RECIFE FPO FIG. 19 BY 0.996
Figure 34. The result of low-time pass filtering the cepstrum of the waveformin Figure 15, a = 0.9980
* .V4LUS20
-32760 •. • "
In F~ure 1, a.-0.997
4-20 81
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- 120
BEG 0.0 SEC MI A 04 - El:s ENO .00409~6 -
FIL 1236 (MEASURED WAV-PORN WD FILE NO.)DSP 1,4,26806
Figure 36. A typical large-angle Pentel lead-break waveform; the angle between the
lead and the surface is 650
4.0
BEG 0. ;"'D .00C .EEN 004096 SEC
Figure 37. A typical small-angle Pentel lead-break waveform; the angle betweenthe lead and the surface Is 400
K ~ ~4-21__ _
4-4
BEG 0.0 3E' MID .00.048 ',EC ENO .084096 SEC
CTl 2346FIL 1635 (MEASURED wAveroSS SD FILE Mo.)DSP 1,4,20868
Figure 38. A Pentel lead-break waveform with secondary Pentel tip impact at alarge angle
AL UES
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CTO IPIL logo (MEASUJRED IAVEPOAJI WD FILE NO.)
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Figure 39. A 200-point sample of a fixture-generated lead-break waveform near theinitial Impulse
4-22
.: . . . . ..- 0 . . . ..
VALUES
too
75
25
0
25
Ds 2.49E- 04 SEC MID10 2.99E-64 SEC ENDO 3.49E-04 SEC
PhL 3015 (SZASURBD SAVEFORN WD PILE NO.)DSP 560,210,32990
Figure 40. A 200-point sample of another fixture-generated lead-break waveformnear the initial impulse
VALUESlag
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leel
DS .00199g SEC MID 0452049 SEC END *.802099 SEC
PIL logo (NIASIJSED WAVUPORI ND PIL; NO.)
*Figure 41. Another 200-point sample of the waveform in Figure 39 near the laterpart of the waveform
L 4-23
4RLUES100
75
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-25
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* 75
BG .401999 SEC KID 00.62649 SEC END .662699 SEC t
CT''IPIL 3010 (MEASURED WAVEfONJI WD FILE NO0.)06? 48666328021
Figure 42. Another 200-point sample of the waveform in Figure 40 near the laterpart of the waveform
4-24
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Figure 45. The result of deconvolving the waveform in Figure 44 by the impulse0 response in Figure 43
L 4-27
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4-28
VALUES1692
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273
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-819
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EPl 4,0,216008,6,790960 SE TE DSCRIP'ON IN IG. 6)LiT E1,1 FLE) FILE 1i WITH THE DESINEDFILTER
£Figure 47. The result of filtering the waveform in Figure 45 with the elliptical filterin Figure 46
42
36
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.. 24z ~STRESS-CORROSIONLAOBE IN
> 16
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THE FOURIER TRANSFORM OF 82)FFT P (CALCULATE THE FOURIER TRANSFORM 18 POLAR COORDINATE)DRE S (DISPLAY THE FOURIER TRANSFORM)
Figure 49. Power spectrum of a stress-corrosion event captured by a resonancetransducer
4-30 -
,ALUES
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BEG 0. E:I .1E-4-E'E0 012
CTX 8192_1V1E11 (SEE THE DESCRIPTION IN FIG. 43)FN INPUT FILE HNE CONTAINHING THE WD NOS. OF THE FILES TO
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NSF S838 6
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FILE N2)DSP S1,1,46000
Figure 50. The average of 31 stress-corrosion waveforms with their initial impulseslined up at the same location; the waveforms were captured with a reso-
m nance transducer -
4-31
VALUES
32768
24576
16364
8192
-8192
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-24576
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TO ST09E THE INVERSE CEPSTIIN(>18
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Figure 51. The result of low-time pass filtering the cepstrum of the averaged*-waveform in Figure 50; no band-pass mapping
4-32
16334
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PCP P. I.INNNNN.300960 (TAXE THE CERST*IN WITH EXPONENTIALWEIGHTI NG AND HANDNPASS MAPPINGPROM JOE KHI To INN 1H.
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N2N3 (N3 IS THE SECONDARY ND FILE NO., #<N2H9990,-
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DS P 31.1.166
Figure 52. The result of low-time pass filtering the cepstrum of the averagedwaveform in Figure 50; band-pass mapping between 100 kHz and300 kHz
p4--
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166.6
66.67
* 52.4 5]
i . e t-'y
S26 O 26
Figure 53. Scatter plots of the first two principal components of the frequency com- ":-pontents of two sets of events after low-time pass filtering in the cepstrail -domain. The two sets of events were generated by (a) rubbing a sandpa- ' .
per on the edge of one end of the aluminum block and (b) rubbing thesandpaper on the facet of the same end of the block
4-34
It
....................................
- 46668
200
-2068
-46 43'
*Figure 54. Scatter plots of the first two principal components of the frequency com-ponents of the two sets of events in Figure 53 without filtering in thecepstrai domain
4-3
- i Ai
I L I
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iLi
-7-
I J* -A-
Figure 55. Scatter plots of the first two principal components of the frequency com-ponents of three sets of events after low-time pass filtering in the cep-stral domain; the three sets of events were generated by (a) rubbing asandpaper on the edge of one end of the aluminum block, (b) rubbingthe sandpaper on the facet of the same end of the block, and (c) lead-breaking
4-36
* - . . .. . . . . . . . . .o
F. see
Xles
r I
llop
Figure 56. Scatter plots of the first two principal components of the frequency com-ponents of the three sets of events in Figure 55 without filtering in thecepstrai domain
4-37
Section 5
CONCLUSION
The key results obtained in this study are summarized below:
Adaptive homomorphic deconvolution seems to work relatively well for AE sig-nais captured with a wide-band flat response transducer with good S/N. Thistechnique is able to clean up multipath and multimode reverberation and ring-down effects rather well. The technique does, however, have some unpleasant adhoc elements, in that several key parameters cannot be determined a priori.Specifically, the decay exponent, needed for exponential weighting to make thesequence a well-behaved minimum phase sequence, is a problem, as are thelinear filter coefficients needed for filtering the cepstral waveform. The appropri- Uate constants can quickly be found with a little experimentation, but the processis non-unique.
Adaptive homomorphic deconvolution seems to work to some degree with a- conventional resonant transducer, particularly when bandpass mapping is em-
ployed. The success of the deconvolution is severely limited, however, because Pof the limited signal bandwidth information provided by the resonant transducer.As can be seen in plots shown in Section 4.6, although pulse compression hasbeen achieved, the reconstructed signal suffers from serious ringing effects dueto the very limited transducer bandwidth.
I * Adaptive homomorphic deconvolution, implemented by high-pass filtering the P__
averaged cepstral domain signal, seems to be effective in providing approximateestimates of the workpiece transfer function, particularly when the original signalis obtained with a wide-band transducer. As noted above, the technique is noteffective when narrow-band resonant transducers are employed, because of thelimited illumination of the cepstral domain afforded by those transducers. Un-fortunately, the wide-band transducers employed in this study are not suitable .for use in practical applications because of their fragility and severely limited sen-sitivity. Their sensitivity is not high enough to be used to obtain signals fromtypical, real AE sources; specifically, they are too insensitive for use with alumi-num stress corrosion V-block sources, or most practical AE sources in general.
- * The final step in employing adaptive homomorphic deconvolution to analyzeacoustic emission signals is to employ ordinary Fourier deconvolution to elimi-nate the effects of transducer ringdown, multipath, etc. Fourier deconvolution,when used to eliminate the workpiece transfer function effects, is very sensitive
'S'- to the precise details of the transfer function. In practical terms, this means thatthe transfer functions must be precisely repeatable from pulse to pulse. In fact, pthe data obtained in this study leads one to believe that there are substantialvariations in the transfer function obtained from both artificial and natural AEsources, particularly when relatively long records of the pulse ringdown signalsare obtained. The transfer functions are more repeatable when relatively shortrecords are used. Preliminary analysis suggests that slight variations in the direc-tion of the signal propagation may be responsible for these effects. A slight varia-tion in the direction of propagation, or in the mix of longitudinal and shear
5-1. . .
waves, will result in changes in the workpiece ringdown response function; thesechanges get larger and larger as the ringdown proceeds. Thus, the later segmentsof long records will suffer progressively increasing distortion from inaccuratedeconvolution. Natural AE signals, since they emanate from evolving crackswhere the crack propagation follows natural grain boundaries, may be expectedto offer some variation in the strength and direction of the emitted shear andlongitudinal waves. Surprisingly, even AE signals carefully generated via artificialmeans (Pental lead breaks) seem to vary in the precise details of their ringdownresponses over relatively long record lengths. The net result is that only rela-tively short (-2048 points) record lengths can be used successfully, either withnatural or artificial AE signal sources.
Pattern recognition, employed as a means of identifying and characterizing AEsources through differences in the microstructure of their waveforms, does notseem to be particularly effective, either when applied to the original waveforms,or when applied to waveforms restored using adaptive homomorphic deconvolu-tion. The original waveforms are heavily contaminated with the workpiecetransfer function effects, and microstructure effects are difficult to separate. Thereconstructed waveforms suffered from ringing distortion because of the limitedbandwidth of the transducers employed. They were also very difficult to separate.
In conclusion, the analytical techniques explored in this research provide severalnew options in processing acoustic emission signals. Specifically, they provide the "means to obtain and employ workpiece transfer functions in deriving the underlyingacoustic emission waveforms. Successful application of these techniques requires the -
use of wide-band transducers that are faithful to the original waveforms and can onlybe employed on relatively short records. Any practical application must await thedevelopment of wide-band accurate transducers with much improved sensitivity over .. ...
currently available transducers.
5-2
....................................
.71-
Section 6
REFERENCES
1. Eitzen, D., Breckenridge, F., Clongh, R., Hsa, N., Proctor, T., and Simmons, J.,"NBS Developments in Qualatative Acoustic Emission Measurements,"AFIDARPA Review of Qualitative NDE, August 1981, Boulder, Colorado.-
2. Tribolet, J.M., Seismic Applications of Homomorphic Signal Processing (EnglewoodCliffs, N.J.: Prentice-Hall, 1979).
3. Oppenheim, A.V., and Schaefer, R.W., Digital Signal Processing (Englewood Cliffs,N.J.: Prentice-Hall, 1975).
4. Brigham, E.O., The Fast Fourier Transform (Englewood Cliffs, N.J.: Prentice-Hall,1974).
5. Weinstein, Clifford J., et al., Programs for Digital Signal Processing (IEEE Press,.0-87942-1 27-4).
F 6. Chen, Y.T., Interactive Pattern Recognition (New York: Marcel Dekker, 1978).
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Appendix B
ILS SOFTWARE MODULES
The ILS Interactive Laboratory SystemTM interactive digital signal processingsoftware package (available through software leasing agreements from Signal Technol-ogy Inc., Santa Barbara, California) was used as the primary software tool in develop- .
ing the signal processing software used in this study. The basic ILS package supplies avery flexible and powerful set of modular software components, implemented in an in-teractive environment featuring considerable graphics feedback. The ILS software pro-vides many generic digital signal processing modules useful in a wide variety of appli-cation areas. When we found that ILS did not prov7,le the necessary functionalityneeded in the acoustic emission application, new ILS modules were written, or 0modifications were made to existing ILS modules to implement the new functionality.These software modules and documentation arf- included on the following pages ofthis Appendix.
• . . .- .
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TM Registered Trademark
B-1
R D-Al59 179 EMPLOYMENT OF ADAPTIVE LEARNING TECHNIQUES FOR THE 2/2DISCRIMINATION OF ACOU.. (U) GENERAL ELECTRIC CORPORATERESEARCH AND DEVELOPMENT SCHENECTA.. J W ERKES ET AL.UNCLSSIFED EC 8 84RD99 N9@14-2-C2031F/O20A/i
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11111L4 JjJ ,1.6
MICROCOPY RESOLUTION TEST CHARTNATIONAL BUREAU OF STANDARDS- 1963-A
o",
Existing ILS commands as supplied by STI:
ADF ARITHMETIC FUNCTIONS ON INTEGER DATAAFP 3-D AREA FUNCTION PLOT OF ANALYSIS DATAANL LINEAR PREDICTION ANALYSIS USING AUTOCORRELATION,
COVARIANCE, OR BURG'S METHODAPI INVERSE FILTER ANALYSIS USING AUTOCORRELATION
METHOD WITH PITCH DETECTION USING CEPSTRAL METHODASG ASSIGN LOGICAL UNIT NUMBER FOR KEYBOARD -
AVG RECORD AVERAGING (MOVING OR EXPONENTIAL)INPUT IS PRIMARY FILE, OUTPUT SECONDARY
BOP BINARY ARITHMETIC OPERATIONS ON FLOATING POINTDATA; OR COMBINE TWO REAL VECTORS INTO ONECOMPLEX VECTOR - TWO FILES INPUT, ONE OUTPUT
BPA PATTERN MATCHING OF TEST AND REFERENCE DATASUPPORTS DYNAMIC PROGRAMMING FOR APPLICATIONSSUCH AS WORD RECOGNITION
CEP CEPSTRUM DISPLAY OF VARIABLE LENGTH FRAMESCLA CURSOR LABELING OF PERIODIC SAMPLED DATACNV CONVOLUTION OF A LONG DURATION TIME SERIES
WITH A FILTER IMPULSE RESPONSE USING SHORTOVERLAPPED FFT'S
COR CORRELATION OF TWO LONG DURATION TIME SERIESUSING SHORT OVERLAPPED FFT'S
CST COMPUTATION OF SAMPLED DATA STATISTICS; PRINTSLOCATION OF PEAK VALUE
CTX EXAMINE OR CHANGE CONTEXT, WHICH IS THE NUMBEROF SAMPLED DATA POINTS PER FRAME OF DATA
CUR X-Y CURSOR, USED IN CONJUNCTION WITH DISPLAYDPM DISPLAY OF ANALYSIS DATA; SUPPORTS VARIABLE
FRAME SIZESDRE DISPLAY REAL OR COMPLEX VECTORS FROM RECORD FILES -DSP DISPLAY OF TIME SERIES; GRIDS AND FRAME LOCATIONS -
EFI ELLIPTIC, BUTTERWORTH AND CHEBYCHEV FILTER DESIGNFDI FREQUENCY SPECTRUM DISPLAY, PROM FFT ON SAMPLED
DATA (MAXIMUM OF 512 POINTS)FFT FAST FOURIER TRANSFORM OF A TIME SERIES; SUPPORTS
CIRCULAR SHIFTS OF THE DATAFIL SPECIFY, CREATE, DELETE BINARY DATA FILES -FLT CONVOLUTION OF A TIME SERIES WITH DIGITAL
FILTERS; SUPPORTS INTEGER OR FLOATING POINTDATA FILES
FPL FREQUENCY PLOT OF SMOOTH SPECTRA FROMANALYSIS FILE -
FTR FORMANT TRACKING OF SPEECH DATA; STORESBANDWIDTH INFORMATION AND SUPPORTS VARIABLEFRAME SIZES
GRD PLOT A GRID FOR FREQUENCY OR AN AXIS FOR TIMEHHH HELP WITH ILS COMMANDSHIS READ DATA FROM RECORD FILES AND PLOT A
HISTOGRAM ON THE SCREENIDC ENTER DATA INTO COMMON BLOCK
B-2
•o .,.- . . ° .° ,. , . . - - . - , . . - , . - . o • . - . - . . . .. . . . o ... ..... -• . ,- -, ,.' '." .'% .. ,. -. ' . ,' ', , *, .*.o ". .*. .. . ", - - , " ., " ,., " ' .. " . .. ". . . .,,.. . . . " - .. ° .. ' -"-- ' -" -, -, Y , ,' " <. -. .- I : / :9§j 4- :. .. : :: . . 2 .:- ".,' .". ..
IFL IDEAL FILTER DESIGN; SUPPORTS CIRCULAR SHIFTOF IMPULSE RESPONSE
ILS CREATE AND INITIALIZE USER COMMON FILEINA INITIALIZATION OF SAMPLED DATA FILE HEADER;
SUPPORTS SPECIFICATION OF LOGICAL END OF FILEWHICH IS USED IF STARTING FRAME =0 AND NUMBER .OF FRAMES-I IN SUBSEQUENT PROGRAMS
LBA LABEL A SAMPLED DATA SEGMENTLBF POINT TO A LABEL FILELCM LIST ILS COMMON (ALL OR PART) 0LFI DESIGNS LINEAR PHASE FINITE IMPULSE RESPONSE
(FIR) FILTERS USING THE REMEX EXCHANGE ALGORITHMLLA LISTS LABEL FILELRE LISTING OF FLOATING POINT DATA; INDEXES TIME
SERIES IN SECONDS AND SPECTRAL DATA IN HERTZLSN DIGITAL-TO-ANALOG CONVERSION *NOT IMPLEMENTED* . S
MDF MODIFY VALUES OF DATA POINTS IN FILESWILL MODIFY FILE HEADERS AND RECORD HEADERS
MDX MULTIPLEXING AND DEMULTIPLEXING OF MULTI-CHANNEL SAMPLED DATA FILES
MRE MANIPULATE RECORD FILES BY EXTRACTING RECORDS,ITEMS AND ELEMENTS 0
MVF DATA MOVING WITHIN A FILE; SUPPORTS ANALYSISFRAMES AND ZEROING OF ORIGINAL DATA
NSI SIMULATION OF NOISY DATA BY ADDING NOISE TO ASIGNAL; GENERATES PSEUDORANDOM NOISE
OPN ALLOCATES AND OPENS RECORD FILESPAN PITCH SYNCHRONOUS ANALYSIS OF SAMPLED DATAPCO PRINCIPAL COMPONENTS ANALYSISPLR SCATTER-PLOT OF DATA ELEMENTS IN RECORD FILESPNS PITCH SYNCHRONOUS SYNTHESIS; INCLUDES IMPROVED
ALGORITHMS WITH GLOTTAL PULSE OR GAUSSIANNOISE EXITATION
PRT PRINT FROM BINARY FILES (OR HEADER)QUR QUEUEING OF FEATURES IN TIME SERIES BASED ON
LABEL INFORMATION FOR PATTERN RECOGNITION.INCLUDES GENERATION OF FEATURE MATRICES FORAPPLICATIONS SUCH AS PATTERN RECOGNITION.
RAN RESIDUE ANALYSIS USING COEFFICIENTS FROM AUTO-CORRELATION OR COVARIANCE ANALYSIS 0
REC ANALOG-TO-DIGITAL CONVERSION INTO A FILEIS NOT IMPLEMENTEDEQUIVALENT HARDWARE AND SOFTWARE EXISTS -'
FOR SOME APPLICATIONSRSO ROOT SOLVING FOR SPECTRAL RESONANCES; STORES
REAL ROOTS FOR HIGH QUALITY SPEECH SYNTHESISRVR REVERSE THE ORDER OF SAMPLED DATA POINTSSDE SPECTRAL-DENSITY ESTIMATION COMMAND
(CROSS OR AUTO)SDI 3-DIMENSIONAL DISPLAY OF SPECTRA; SUPPORTS
INTEGER TIME SERIES, FLOATING POINT TIMESERIES OR FLOATING POINT SPECTRA INPUT FILES 0
SGM SPECTROGRAM DISPLAY OF ANALYSIS DATA; SUPPORTSVARIABLE FRAME SIZES AND ERASES BEFORE DISPLAY
B-3
SIF FUNDAMENTAL FREQUENCY EXTRACTION USING SIFTALGORITHM
SHE CALCULATES STATISTICS OF DATA IN FEATURE RECORDSSNS SYNTHESIZE SAMPLED DATA FROM ANALYSIS DATASPL 3-DIMENSIONAL SPECTRAL PLOT OF ANALYSIS DATA;
SUPPORTS VARIABLE FRAME SIZESSRE STORE RECORDS INTO SECONDARY FILE FROM
KEYBOARD INPUT, PRIMARY SAMPLED DATA FILE ORPRIMARY ANALYSIS FILE
SSP FREQUENCY SPECTRUM DISPLAY FROM FFT OF INVERSEFILTER COEFFICIENTS
TBL SET UP DIRECTORY TABLE FOR ILS FILE SYSTEMTFU PROGRAM FOR CREATING TEST DATA IN A FILE
(FILE MUST BE CREATED FIRST)TLA COPY LABELS MEETING A GIVEN SPECIFICATION INTO
A SECONDARY LABEL FILETRE TRANSFER OF FLOATING POINT DATA; SUPPORTS
CHANGES IN RECORD SIZETRF DATA TRANSFER BETWEEN FILES; SUPPORTS ANALYSIS
FRAMESTRM SETTING OF TERMINAL CHARACTERISTICS; SUPPORTS
NUMBER OF GRAPHIC INPUT TERMINATORS AND THEHP2648 TERMINAL IN NATIVE MODE. ALSO PRINTSSYSTEM TIME AND DATE AND WILL LABEL A PLOT.WILL CLEAR SCREEN OR PUT TERMINAL IN ALPHA MODE
TSI TEST SIGNAL, GENERATE SAMPLED DATA, LABELOR RECORD FILES.
TTL TRANSFERS MARKED SECTION OF SAMPLED DATA TOTHE SECONDARY FILE WITH OPTIONAL LABELING
UOP UNARY OPERATIONS, PHASE UNWRAPPING OF FFT DATA;USES A MUCH IMPROVED ALGORITHM. MANY OTHERMANIPULATIONS OF FLOATING POINT DATA
VDI VARIABLE DISTANCE THRESHOLD EVALUATIONVER VERIFY HEADER BLOCK IN SAMPLED DATA OR
ANALYSIS FILEVTR PLOT A VOCAL TRACT FROM SECONDARY ANALYSIS
FILE OR USER'S COMMONXPA EXPAND, INTERPOLATE OR DOWNSAMPLE PRIMARY
SAMPLED DATA FILE FOR HIGHER OR LOWER SAMPLINGFREQUENCIES, BY INTERLEAVING ZEROS WITH THEORIGINAL DATA OR SKIPPING DATA
XTR READ DATA FROM PRIMARY RECORD FILE AND COMPUTEMAXIMUM OR MINIMUM VALUES
New ILS commands developed and used in the course of thisresearch.
$ APF - MERGES GRAPHIC OUTPUT FILES..WILL ALTERNATELYMERGE INTO A USER CHOSEN FILE NAME.
AMP - HISTOGRAMS WITH STATISTICS FOR SAMPLED DATA FILES
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. . . .. . .
S
$ CLR PUTS AN ADM TERMINAL IN ALPHA MODE THENCLEARS SCREEN AFTER GRAPHICS SESSION
$ CPF - REASSIGNS GRAPHIC OUTPUT TO THE TERMINAL$ GRA - PUTS AN ADM TERMINAL IN GRAPHICS MODE
THEN CLEARS SCREEN .............$ CXP - MODIFICATION OF CEP TO WRITE DATA WHICH WAS
PREVIOUSLY PLOTTED, TO A FILE.
$ HED - LIST CONTENTS OF THE SPS PORTION OF ILS HEADER$ HFL - APPEND HEADER TO YOUR DATA$ HPF - PROCESSES GRAF.TMP FILES RECOGNIZING FORM FEED
NOT TO BE USED WITH OVERLAYS. DEVELOPED FORUSE WITH HSP.
$ HSP - HISTOGRAM OF DATA PEAKS AND ENERGY CONTENT OFDATA FILES.
$ ITN - INSERTS TEST NAME,COMMENTS AND ISPS HEADERVALUES INTO ISPS PORTION OF HEADER
$ LAB - LABELS FOR PLOTS. CREATES A GRAF.TMP FILE TOBE MERGED TO PROVIDE HORZ _VERT LABELING.
F $ MST - WRITES STATISTICS FROM SAMPLED DATA FILESAS FROM ILS COMMAND "$ CST", TO THE FILE"CSTAT.TMP" WITH LEGEND AND HEADINGS.SUBSEQUENT USES APPEND DATA.
$ OPF - ASSIGNS GRAPHIC OUTPUT TO A FILE NAMED GRAF.TMP$ PPF - PROCESSES AND PRINTS GRAF.TMP FILES$ RR - LISTS COMMANDS WHICH USE RECORD DATA$ RST - WRITES STATISTICS FROM RECORD DATA FILES
AS FROM ILS COMMAND "$CST", TO THE FILE"CSTAT.TMP" WITH LEGEND AND HEADINGS.SUBSEQUENT USES APPEND DATA.
$ RTS - RECORD DATA TO SAMPLED DATA FOR DISPLAY PURPOSES$ STN - SEARCHES A DIRECTORY FOR WD FILES FROM A
GIVEN TEST, ALTERNATELY USES WD NUMBERS FROM -}A FILE.
$ TRM - TRM M WILL PRINT VERTICALLY IF N1 IS NEGATIVE$ WIN - APPLIES FULL OR PARTIAL HANNING WINDOW
TO SAMPLED DATA$ WTN - WRITES ISPS PORTION OF FILE HEADER TO
SECONDARY FILE
$ XCP - COMPUTES COMPLEX CEPSTRUM FROM INPUT WAVEFORM,(INCLUDES EXPONENTIAL WEIGHTING, AND BANDPASS -'-
MAPPING)
Specialized Interactive "Recipes" using ILS commands
L B-5 . .,. . . ,*..°....* .****.**. .*/ * ,:* ~ .~.*. *. .. . ..-
XCPILOW.COM -an ILS "recipe" that implements a forward complexcepstrum, low-pass filters the cepstrum, and finally does aninverse complex cepstrum.
$1 LOW-PASS CEPSTRUM AND INVERSE TRANSFORM$ ON CONTROLY THEN GOTO CLEANUP$ ON ERROR THEN GOTO CLEANUP$ IF P1 .EQS. THEN INQUIRE P1 'INPUT FILE NUMBER?-$ IF P2 .EQS. "THEN INQUIRE P2 "OUTPUT FILE NUMBER?'-*$ IF P3 .EQS. "THEN INQUIRE P3 'STARTING CHANNEL NO.?*$ IF P4 .EQS. "THEN INQUIRE P4 "ENDING CHANNEL NO.?"$ IF P5 .EQS. "THEN INQUIRE P5 "CONTEXT?'$ CTX 'P5'$ FIL SOCZ9996, ,lCZ9997, ,l
$FIL 'P1'$FIL S9996$XCP Z'P3','P41$FIL 9996$FIL S9997$XCP is
$ RENAME WD9997. WD'P21.$CLEANUP:$dele/NOCONFIRM WD9996.;l
XCPIHIGH.COM -an ILS 'recipe' that implements a forward complex2* cepstrum, high-pass filters the cepstrum, and finally does an
inverse complex cepstrum.
$1 HIGH-PASS CEPSTRUM AND INVERSE TRANSFORM$ ON CONTROLY THEN GOTO CLEANUP$ ON ERROR THEN GOTO CLEANUP$ IF P1 .EQS. w", THEN INQUIRE P1 'INPUT FILE NUMBER?'$ IF P2 .EQS. "THEN INQUIRE P2 'OUTPUT FILE NUMBER?'$ IF P3 .EQS. "THEN INQUIRE P3 'U.P. OF 1st BAND?'$ IF P4 .EQS. "THEN INQUIRE P4 'L.B. OF 2nd BAND?'
*$ IF P5 .EQS. "THEN INQUIRE P5 'CONTEXT?'* $ CTX 'P5'
$FIL SOCZ9996,,lCZ9997,,lCZ9998,,1
$FIL 'P1'$FIL S9996
B-6
XCP Zl1 'P3'$FIL 9996
$ FIL S9997$ XCP Z'P4' 'P5'$ FIL 9997$ FIL S9998
CPis -
$ RENAME WD9998. WD'P21.$CLEANUP:$ dele/NOCONFIRM WD9996.;j$ dele/NOCONFIRM WD9997.;l
XCPIPLOW.COM - an ILS "recipe" that implements bandpass mappingfor bandpass limited signals, followed by a forward complexcepstrum, a low-pass filtering operation on the cepstrum, andfinally an inverse complex cepstrum.
$1 LOW-PASS CEPSTRUM AND INVERSE TRANSFORM$1 MODIFIED FOR BAND-PASS SYSTEM$ ON CONTROLY THEN GOTO CLEANUP$ ON ERROR THEN GOTO CLEANUP$ IF P1 .EQS. "THEN INQUIRE PI -INPUT FILE NUMBER?"$ IF P2 .EQS. "THEN INQUIRE P2 -OUTPUT FILE NUMBER?"$ IF P3 .EQS. 00 THEN INQUIRE P3 OSTARTING CHANNEL NO.?-$ IF P4 .EQS. ""THEN INQUIRE P4 PENDING CHANNEL NO.?-$ IF P5 .EQS. ""THEN INQUIRE P5 -CONTEXT?-$ CTX 'P51$ FIL SOCZ9996,,lCZ9997, ,1
$ FIL 'P1'$ FIL S9996$ XCP PZ'P3','P4'$ FIL 9996$ FIL S9997$ XCP ISP$ RENAME WD9997. WDIP21.$CLEANUP:$ dele/NOCONFIRM WD9996.;l
XCPIPHIGH.COM - an ILS "recipe" that implements bandpass mappingfor bandpass limited signals, followed by a forward complexcepstrum, a high-pass filtering operation on the cepstrum, andfinally an inverse complex cepstrum.
$1 HIGH-PASS CEPSTRUM AND INVERSE TRANSFORM$1 MODIFIED FOR BAND-PASS SYSTEM$ ON CONTROLY THEN GOTO CLEANUP
(2 B-7*
p7
$ ON ERROR THEN GOTO CLEANUP$ IF P1 .EQS. "" THEN INQUIRE P1 wINPUT FILE NUMBER?*$ IF P2 .EQS. w" THEN INQUIRE P2 "OUTPUT FILE NUMBER?-3$ IF P3 .EQS. w" THEN INQUIRE P3 NU.P. OF 1st BAND?"$ IF P4 .EQS. w" THEN INQUIRE P4 "L.B OF 2nd BAND?"$ CTX PSEQS. w* THEN INQUIRE P5 "CONTEXT?"
$ T P5'$ FIL SOCZ9996,,1S CZ9997,1
* CZ9998,,1
$ FIL 'P1'$ FIL S9996$ XCP PZ1,'P3'$ FIL 9996$ FIL S9997$ XCP PZ'P4','P5'$ FIL 9997$ FIL S9998$ xCP ISP --
P$ RENAME WD9998. WD'P2'.$CLEANUP:$ dele/NOCONFIRM WD9996.;1$ dele/NOCONFIRM WD9997.;l
FDECON.COM -an ILS *recipe" that implements Fourier Deconvolution4
$1 FOURIER DECONVOLUTION$ ON CONTROLY THEN GOTO CLEANUP5$ ON ERROR THEN GOTO CLEANUP$ IF P1 .EQS. -- THEN INQUIRE P1 "INPUT A-FILE NUMBER?"$ IF P2 .EQS. "" THEN INQUIRE P2 "INPUT B-FILE NUMBER?-$ IF P3 .EQS. "" THEN INQUIRE P3 "OUTPUT FILE NUMBER?"$ FIL S9993$ OPN S5$ FIL 'PlV$ $SRE 1,1$ FIL 'P21$ FIL S9994$ SRE 1,1$ FIL 9993$ FIL S9995$ FFT$ FIL 9994$ FIL S9996$ FFT$ FIL 9995$ FIL B9996$ FIL S9997$ BOP D$FIL 9997
B-8
.7. . . .
$ FIL S'P3'$ OPN Si$ FFT I$CLEANUP:$ dele/NOCONFIRM WD9993.;1$ dele/NOCONFIRM WD9994.;l$ dele/NOCONFIRM WD9995.;l$ dele/NOCONFIRM WD9996.;l
$ dele/NOCONFIRM WD9997.;l
FDECONP.COM - Sn ILS 'recipe' that implements Fourier* Deconvolution on bandpass mapped waveforms.
$1 FOURIER DECONVOLUTION WITHIN A FREQUENCY BAND 0$ IF P1 .EQS. "" THEN INQUIRE P1 'INPUT A-FILE NUMBER?'$ IF P2 .EQS. "THEN INQUIRE P2 *INPUT B-FILE NUMBER?'"$ IF P3 .EQS. "THEN INQUIRE P3 -OUTPUT FILE NUMBER?'$ IF P4 .EQS. "THEN INQUIRE P4 'FREQUENCY LOWER LIMIT?'$ IF PS .EQS. "THEN INQUIRE P5 'FREQUENCY UPPER LIMIT?'$ ON CONTROLY THEN GOTO DELETECOMMAND
*$ OPEN/WRITE OUT FDE.COM$ WRITE OUT =$ON CONTROLY THEN GOTO CLEANUP"$ WRITE OUT '$ON ERROR THEN GOTO CLEANUP'$ WRITE OUT w$ FIL S9993'$ WRITE OUT '$ OPN S5-$ WRITE OUT '$ FIL ''P1''$ WRITE OUT 'S SRE 1,1"$ WRITE OUT '$ FIL ''P2''$ WRITE OUT '$ FIL S9994'$ WRITE OUT w$ SRE 1,1'
p$ WRITE OUT '$ FIL 9993'$ WRITE OUT '$ FIL S9995"$ WRITE OUT "$ FFT'$ WRITE OUT w$ FIL 9994'$ WRITE OUT "$ FIL S99960$ WRITE OUT w$ FFT'$ WRITE OUT '$ FIL 9995'$ WRITE OUT *$ FIL B9996"$ WRITE OUT w$ FIL S9997'$ WRITE OUT '$ BOP DF'$ WRITE OUT w'1P1j'5.
*$ WRITE OUT w$ FIL 9997'$ WRITE OUT '$ FIL S''P3'$ WRITE OUT '$ OPH Si'
6$ WRITE OUT 'SFFT I"$ WRITE OUT w$CLEANUP:*$ WRITE OUT w$ dele/NOCONFIRM WD9993.;1'$ WRITE OUT '$ dele/NOCONFIRM WD9994.;1'L$ WRITE OUT '$ dele/NOCONFIRM WD9995.;i'$WRITE OUT '$ dele/NOCONFIRM WD9996.;1'
$ WRITE OUT '$ dele/NOCONFIRM WD9997..;1'$CLOSE OUT
[9 B-9
701
$ FDE.COM$DELETECOMMAND:DELETE/NOCONFIR4 FDE.COM;-
* AVERG.COM - an ILS "recipe" that implements an averagingoperation ona series of candidate waveforms.
$ ON CONTROLY THEN GOTO CLEANUP$ ON ERROR THEN GOTO CLEANUP$ IF P1 .EQS. '" THEN INQUIRE P1 "INPUT FILE?"$! INPUT FILE CONTAINS WD NUMBERS, ONE PER LINE, OF FILES TO BE
* AVERAGED* $ IF P2 .EQS. "" THEN INQUIRE P2 'OUTPUT FILE NUMBER?'
$ OPEN/READ IN 'P1'$ COUNT=0$ FIL S9995$ $OPN S3
* $LOOP:$ READ/ENDOFFILE=THATSALL IN NUM
* $ COUNT=COUNTI-$ FIL INUM'$ SRE 1,1$ GOTO LOOP4
- $THATSALL:$ FIL 9995
- $FIL S9996*$ AVG 1,'COUNT'-$ FIL 9996
$ FIL S9997$ TRE 'COUNT',1$ FIL 9997$ FIL S'P2'$ RTS 1,1$CLEANUP:
* $ dele/NOCONFIR4 WD9995.;1$ dele/NOCONFIRM WD9996.;1$ dele/NOCONFIRM WD9997.;l$CLOSE IN
* Special Purpose ILS Software Modules created for this Study
x CP.FOR
B- 10
C... INTERACTIVE LABORATORY SYSTEM
C... ILS COMMAND PROGRAM ** XCP **C...
PROGRAM XCPC...
.. IMPLICIT INTEGER (I-N)C*..C.. START OF DOCUMENTATIONC.. p.•e.C... SPECIAL VERSION TO USE ENTIRE FILECo.*
C... COMMAND FORMAT:C..*C... XCP IZ,I,F][S]NI,N2 SC.O.C.0. ALPHABETIC ARGUMENTS:C .*C.0. Z - ZERO CEPSTRUM RECORD FROM Ni TO N2
f C... I - INVERSE CEPSTRUM ,o.
C... F - CREATE TEST FILE PC..* S - USED WITH [I], OPTIONAL PHASE SHIFTC... P - PREPROCESS WITH FREQUENCY LIMITC.O.C... NUMERIC ARGUMENTS:C.."
* C... Ni - STARTING FRAMEC..* N2 - NUMBER OF FRAMESC.. WITH OPTION [Z]C... Ni - FIRST POINT TO ZEROC... N2 - LAST POINT TO ZEROCC... N3 - ASK FOR ALPHAC... WITH OPTION (P]C... N4 - LOWER FREQUENCY
*C..* NS - UPPER FREQUENCYC...C... END OF DOCUMENTATIONC ...
COMMONPI,TWOPI,THLINC,THLCON,NFFT,NDUM,NN,L,H,H1,DVTMN2,AMULT
COMMON /CLBF/ INSFLG,LCLBF, ICLBF (40)COMMON /ILSA/ NBCW,NCWBK,NDPBK,NDPF,NBDP,NCWFH,
- 1 KBU,KBUIN,LPU,LUGI,LUGO,NSC,CWSC,2 NBA2D,MIDA2D,ICTIM(4),ICDAT(6)
COMMON /ILSB/ IA(4) ,N1,N2,N3,N4,N5,N6,N7,N8,N9,NIO,Nll,N12COMMON /ILSC/ IASAV(4),NISAV,N2SAV,N3SAVN4SAV,N5SAV,N6SAV,
1 N7SAV,N8SAVN9SAV,N1OSAV,N11SAVN12SAVCOMMON /ILSE/
IFLPA(16) ,LENPALFILPANFLPA,IDKPAIDKDPA,IDPACOMMON /ILSF/
IFLSA(16) ,LENSA,LFILSA,NFLSA,IDKSAIDKDSA,IDSA• .COMMON /ILSH/ FS,M,MP1,M02,N,NSPBK,NSHFT,ICON,ISF,IHAM,LAN
B-1l• " ... ..* .
COMMON /ILSI/ LRH,IEX,ISTAN,NAN,IDF(5) ,NP,IVL,ICCOMMON /ILSJ/ RC(30) ,A(30) ,R(30) ,F(10) ,B(10)
C.0.0-COMMON /FLC1/ IFL1(16) ,LEN1,LFIL1,NFL1,IDK1,IDKD1,ID1COMMON /FLCM/
IFLC(16) ,LENC,IFLALF(4) ,LENALF,IFLX,IFLVLENCOMC..
* * DIMENSION IY(16384) ,IR(16896) ,IS(16896) ,IX(16384)* * DIMENSION Y(16384) ,X(16384) ,DUM(16384)-
DIMENSION IHR(128) ,IHW(128) -
DIMENSION IOPT(5) ,ICHSTR(5)EQUIVALENCE (IHR(70) ,SCALR) ,(IHW(70) ,SCALW)EQUIVALENCE (IHR(74) ,ACEP) ,(IHW(74) ,ALPHA)
C.00CC..
DATA SCL1/1.0/DATA Il,I2,I3,14,I5,Il1,119,I30/1,2,3,4,5,11,19,30/
* DATA ICHSTR(1) ,ICHSTR(2) ,ICHSTR(3) ,ICHSTR(4)/2HZ ,2HI ,2HS,2HF/
DATA ICHSTR(5)/2HP/DATA IHW(75),IHW(76)/0,0/DATA IFLG,IIBW,IIBR,IOVERFLO/4*0/DATA LIX,LIY,LIR,LIS/2*16384,2*16896/DATA ICHA,ICHNP,ICHS,ICHR/2HA ,2HNP,2HS ,2HR/DATA SCL0/0.0/
CALL RCOMM* C...
C..* INITIALIZATION DATA*CALL AFARG(IA,I1,I4,ICHSTR,IOPT,15)
Ce.0C... CHECK OPTIONSC ..
IF(IOPT(1) .EQ.1)THENCo.*C... ZERO PORTION OF CEPSTRUM
IMODE =1ELSE IF (IOPT(2).EQ.1)THEN
* . Co. *C... INVERSE CEPSTRUM
IMODE=2ELSE IF (IOPT(4) .EQ.1)THEN
C.. *C... CREATE TEST FILE
IMODE=4* * ELSE
* C.00C.00 FORWARD CEPSTRUM OR PREPROCESS
IMODE=0END IF
C*4.
B- 12
QN.
r0Co.*. INVERSE CEPSTRUM WITH PHASE SHIFT
IF(IMODE.EQ.2.AND.IOPT(3) .EQ.1)IMODE=3C..C... SET FRAM4ES TO DEFAULT TO WHOLE FILECo.*
DO 10 I=1,4IF(IOPT(I) .NE.0)GOTO 11
10 CONTINUEC..* FIND CEPSTRUM ...... SET UP NUMBER OF POINTS
IF(Nl.EQ.0.AND.N2.EQ.0)THENN1A=0N2A=l
ELSEN1A=NlN2A=N20
END IFGOTO 12
C.00 OPTIONS [I] AND [Z] USE THE ENTIRE FILE11i IF(IOPT(4).EQ.1)THEN
NPTS=2048 .LFILSA=20 48/NDPBKLFRAM=NDPFNFRAM=2 04 8/NDPFGOTO 260
END IF-NlA=0N2A=l
* .. C...12 CALL CHKFL(NFLPA,IDKPA,IFLPA,LENPA,LFILPA,IHR,ICHS,IERR)
IF(IERR.NE.0) GO TO 310C..C ... GET SAMPLING FREQUENCYC ...
ISF=IHR( 62)IPWR=IHR( 61)CALL SFCNV(FS,ISF,IPWR,I1)CALL ANCHK(NSC,N1A,N2A,N1SAV,N2SAV,NSCA,ISTAN,1 NAN,NDPF,NSDBK,LFILPA)I STFR=N1 SAVNFR=N2SAV
C .*C.*. GET NUMBER OF POINTS ..... TRUNCATE TO A POWER OF 2C...
CALL FTOP(N1SAV,N2SAV,NSC,NDPF,STPT,PTS,ENDPT)9* NPTS=IFIX (PTS+0 .5)
INDX=16 38420 IF(NPTS.GE.INDX)THEN
NPTS=INDX
ELSE GOTO 30 -.qINDX=INDX/2
11 B- 13
V--7k7wx
END IFV. GOTO 20
Co. -
c... CONVERT BACK TO FRAMESC.0030 PTS=FLOAT(NPTS)
CALL PTOF(STPTPTS,NDPF,NSC,ISTFR,NFR)NPTX=NPTSNPTY=NPTSIST-ISTFRLST=ISTFR+NFR-1
C... SET SCALEIF(IMODE.EQ.1) THEN
SCALE=1.0ELSE IF(IMODE.EQ.0)THEN
SCALE =1.0ELSE IF(IMODE.EQ.2.OR.IMODE.EQ.3)THEN
SCALEmSCALREND IFCALL GETD(NSC,ISTFR,NPTS,NPTY,IR,LIR,IY,IIBR,
1 IFLPAILENPA,LFILPA)IF(IIBR.LT.0)GOTO 260
C .0CALL M12R(IY,YINPTS,SCALE)
200 CONTINUEC... ALL POINTS READ
LFILSA=LFILPA260 IFLGO=2
ITYPE=-1CALL CHKFL(NFLSArIDKSA,IFLSA,LENSA,LFILSA,IHW,ITYPE,IFLGO)
* ITYPE=ICHNP- . CALL SETUP(IFLSA,LENSALFILSA,NFRAM,LFRAM,NCWFH,IHW,ITYPE)* IF(NFRAM.EQ.-1)GOTO 310
C..*C.00
IHW(62) = IHR(62)IHW(61) = IHR(61)IHW(63) = -32000IF(IOPT(5) .EQ.1) THEN
IF(IMODE.EQ.0)THENF1=FLOAT(N4)F2=FLOAT (N5)IHW(75) =N4IHW(76) =N5
ELSE lFOTIR7)F1=FLOAT(IHR(75))
IHW (7 5) =IHR (7 5)IHW(76) =IHR(76)
END IFELSE
IHW(75) -0IHW(76) =0
B-i14
END I FIF (IMODE .EQ. 1) SCALW=SCALR
Co* NCEP=NPTS
AMULT-ACEP
C... MAP FORWARD TRANSFORMC.**
IF(IOPT(5) .EQ.1.AND.IMODE.EQ.0) THENCALL CMAP(NCEP,YX,FS,F1,F2,IMODE)
C STOPCALL MR2R(X,Y,NCEP,I1)
END IFCALL CCPC(NCEP,YX,IMODE)
Co..*C.0. MAP INVERSE???C.**
IF(IOPT(5) .EQ.1.AND. (IMODE.EQ.2.OR.IMODE.EQ.3) )THENCALL CMAP(NCEP,X,Y,FS,F1,F2,IMODE)CALL MR2R(Y,X,NCEP,I1)
ir END IFC...C.00 X IS THE OUTPUT VARIABLEC.O.C... SCALE OUTPUT VARIABLEC.O
IF(IMODE.EQ.1)GOTO 275 ..
CALL FPPIC(X,I1,NPTS,JLOC)SCALE=ABS(32767 ./X(JLOC))
* SCALW=lo/SCALEC... NOW THAT OUTPUT SCALE IS KNOWN,,WRITE HEADERC... SCALE IS EQUIVALENCED TO HEADER LOCATION 70C.00 WHEN THE ZERO OPTION IS USED, NO SCALING IS DONE FC... ALSO SET ALPHA=AMULT TO STORE IN HEADERC.O.275 ALPHA-AMULT
CALL WHEAD (IHW, IFLSA, LENSA)* co.
C.00 CONVERT TO INTEGER. .SCALE FOR MAXIMUM ACCURACYC.O.
CALL MR21 (X,IX,NPTS,SCALE)IFRAM-1CALL WRITD(NSC,IFRAM,ISDB,NPTS,IS,LIS,IX ,IIBW,1 IFLSArLENSArLFILSA)
280 CONTINUEC.00 DUMP BUFFER
IIBW=-IIBWCALL WRITD(NSCIFRAM,ISDB,NPTS, IS,LIS,IX,IIBW,1 IFLSAILENSA,LFILSA)
100 CONTINUEii.999 CONTINUE310 CALL WCOMM
CALL EXILSEND
LB- 15
.....................................................
List of Fortran Modules needed to compile XCP.FOR
AMODSQ -FFA .FFS I" '
FFT .FFT842 IMRlDF .ORDIORD2 .PHADVT ------- contained in CCEPS.FOR and CCXTRA.FORPHAUNW IPHCHCK I -PPVPHA .R2TR -R2TX ,
R4SYN IR4TRR4TXR8SYNR8TR .R8TX "RPSPCVAL I 5--SHIFTF -
CMAP.FOR
SUBROUTINE CMAP(NSAMP,Y,B,FS,F1,F2,MODE)C..C... MAPS FILTERED DATA WITH A SELECTED FREQUENC- RANGEC... INTO ENTIRE SPECTRUM FOR FORWARD CEPSTRUM OR ENTIREC... FREQUENCY RANGE INTO SELECTED BAND FOR INVERSE CEPSTRUMC...C... ARGUMENTS:C... NSAMP - NUMBER OF SAMPLESC... Y - INPUT VARIABLE TIME SERIESC... B - OUTPUT VARIABLE TIME SERIESC... FS - SAMPLING FREQUENCYC... Fl - LOWER FREQUENCY BOUNDC... F2 - UPPER FREQUENCY BOUNDC... MODE - IMODE FROM CEPSTRUMC.00
C... VARIABLE LISTC... DELF FREQUENCY INCREMENTC... DELT TIME INCREMENTC... DINT INTERPOLATING FRACTIONC... FINT REAL LOCATION OF LOWER FREQUENCY BOUND
B-16 I
C... FMAX MAXIMUM FREQUENCYC... ILOC INTEGER LOCATION OF INTERPOLATED FREQUENCYC... INTF1 INTEGER LOCATION OF LOWER FREQUENCY BOUNDC... INTF2 INTEGER LOCATION OF UPPER FREQUENCY BOUND •C... IOFSET ADDER TO LOCATE FREQUENCY RANGEC... IPOS LOCATION OF REAL PART OF LOWER INTERPOLATION PAIR
* C... NINT NUMBER OF FREQUENCIES TO MAP(F2-Fl), DOES NOTC INCLUDE FlC... R1 REAL PART OF LOWER INTERPOLATION PAIRC.. R2 REAL PART OF UPPER INTERPOLATION PAIR 0Co.. RATIO RATIO OF MAPPED FREQUENCIES TO TOTAL FREQUENCIESC... VLOC LOCATION OF INTERPOLATED FREQUENCYC... Xl IMAGINARY PART OF LOWER INTERPOLATION PAIRC... X2 IMAGINARY PART OF UPPER INTERPOLATION PAIR
DIMENSION Y(l),B(NSAMP+2)DELT=I./FSDELF=FS/NSAMPNFREQ=NSAMP/2.FMAX=FS/2.
C...C... WHERE IN THE FREQUENCY ARRAY IS THE LOWER FREQUENCY BOUNDCo
FINT=Fl/DELFINTFI=IFIX(FINT)IF(FLOAT(INTFl).LT.FINT)INTFI=INTFl+1K INTF2=IFIX(F2/DELF)NINT=INTF2-INTFI 0_
IOFSET=2*INTFI+1C ...C ... CONVERT TO FREQUENCY DOMAINC..C
1 C... SUBROUTINE FFA REPLACES THE REAL VECTOR B(K), p
C... WITH ITS FINITE DISCRETE FOURIER TRANSFORM. THE DC TERM ISC... RETURNED IN LOCATION B(l) WITH B(2) SET TO 0. THEREAFTER,
l* THEC... JTH HARMONIC IS RETURNED AS A COMPLEX NUMBER STORED ASC... B(2*J+l) + I B(2*J+2). NOTE THAT THE N/2 HARMONIC IS 0RETURNED
C... IN B(N+l) WITH B(N+2) SET TO 0. HENCE, B MUST BEDIMENSIONED
* C... TO SIZE N+2.C... SUBROUTINE IS CALLED AS FFA (B,N) WHERE N=2**M AND B IS ANCo.. N TERM REAL ARRAY. pCo.*
CALL FFA(Y,NSAMP)
C... Y NOW CONTAINS FREQUENCY VALUESC... MAP SELECTED RANGE INTO ARRAY B
IF(MODE.EQ.0)THENB(l) =Y(IOFSET)B(2) =Y(IOFSET+l)
B--17
. . . . . . . . . . . . .. . . *...
C..RATIO=FLOAT(NINT) /FLOAT(NFREQ)
C TYPE *,DELT,DELFrNFREQ,FMAX,.ATIOC TYPE *,INTF1,INTF2,NINT,IOFSET .4
DO 100 KJ=1,NFREQVLOC=FLOAT (KJ) *pRTIOILOC=IFIX (VLOC)DINT=VLOC-ILOCIPOS=2 *ILOC+IOFSETR1=Y (IPOS) -
R2=Y( IPOS+2)X1=Y (IPOS+1)X2=Y( IPOS+3)B(2*KJ+1) =R1+DINT* (R2-R1)B(2*KJ+2) =Xl+DINT* (X2-X1)
100 CONTINUE9999 FORM4AT((I8,4(4F7.0,2X))/)C...C... SHIFT PHASE
CALL SHIFTF (B,NSAMP)C WRITE(3,9997)9997 FORMAT(8X,4(5X,'INPUT19X,#SHIFTED',4X))C WRITE(3,9998)9998 FORMAT(' FREQ 1,4(2(l REAL IMAG ')C WRITE(3,9999)(J,(Y(2*J+1),Y(2*J+2),B(2*J+1),B(2*J+2),C 1 Y(2*J+3) ,Y(2*J+4) ,B(2*J+3) ,B(2*J+4),C 2 Y(2*J+5),Y(2*J+6),B(2*J+5),B(2*J+6),4C 3 Y(2*J+7),Y(2*J+8),B(2*J+7),B(2*J+8)),C 4 J=0,NFREQ-3,4)
ELSERATIO=FLOAT (NFREQ) /FLOAT (NINT)B(1)=0.B(2)=0.DO 200 KJ=1,NFREQ
IF(KJ.LT.INTF1.OR.KJ.GT.INTF2) THENB(2*KJ+1) =0.B(2*KJ+2) =0.
ELSE INDX=KJ-I NTF1VLOC=RATIO*FLOAT( INDX)ILOC=IFIX (VLOC)DINT=VLOC-ILOCIP05=2*ILOC41
R2=Y (IPOS)X1=Y (IPOS+1)MG
X2=Y (IPOS+3)B(2*KJ+1) =Rl+DINT*(R2-R1) -
B(2*KJ+2) =X14DINT*(X2-XI)END IF
200 CONTINUE _
Coe*END IF
B- 18
:4fi
C..* SUBROUTINE FFS SYNTHESIZES THE REAL VECTOR B(K), WHERECo.. K=1,2l ... pN. THE INITIAL FOURIER COEFFICIENTS ARE PLACED INC.O. THE B ARRAY OF SIZE N+2. THE DC TERM IS IN B(1) WITHC.0. B(2) EQUAL TO 0.C... THE JTH HARMONIC IS STORED AS B(2*J+1) + I B(2*J+2).C..* THE N/2 HARMONIC IS IN B(N+1) WITH B(N+2) EQUAL TO 0.C... THE SUBROUTINE IS CALLED AS FFS(BN) WHERE N=2**M AND ,
C.00 B IS THE N TERM REAL ARRAY DISCUSSED ABOVE.
CALL FFS(B,NSAMP)C..
RETURNEND
CCEPS .FOR
r CC----------------------------------------------------------------------- ----
t. C SUBROUTINE: CCEPSC SUBROUTINE TO COMPUTE THE COMPLEX CEPSTRUM OF A SEQUENCE X(N)C---------------------------------------------------------------------
CSUBROUTINE CCEPS(NX,X,ISNX,ISFX,ISSUC,CX,AJX)
CDIMENSION X(1) ,CX(1) ,AUX(l)COMMON PI,TWOPI,THLINC,THLCON,NFFT,NPTS,N,L,H,H1,DVTMN2LOGICAL ISSUCNPTS=NFFT/2N=12L=2**NH=FLOAT (L) *FLOAT (NFFT)H1=PI/HISSUC= .TRUE.I SNX=1
CDO 10 I=1,NX
CX(I)=X(I)AUX(I)=FLOAT(I-1) *X(I)
10 CONTINUEIN ITL=NX +1I END=NFFT+2DO 20 I=INITL,IEND
CX (I) = 0 *AUX(I) =0.0
20 CONTINUE
B- 19
CCALL PFA(CXNPFT)CALL FFA (AUX ,NFFT)
CIF(CX(1) .LT.0.0)ISNX=-
C10-iDVTMN2=0.0I END=NPTS+1DO 30 I=1,IEND
I0=10+2IE-IO+1ANAGSQ=AMODSQ(CX(IO) ,CX(IE))PDVT=PHADVT(CX(IO) ,CX(IE) ,AUX(IO) ,AUX(IE) ,AIAGSQ)AUX (10)=AMAGSQAUX (IE) =PDVTDVTMN 2-DVTMN2+PDVT
*30 CONTINUEDVTMN2= (2**DVMN2-.AUX (2) -PDVT) /FLOAT (NPTS)
CPPDVT=AUX (2)PPHASE=0 .0PPV=PPVPHA(CX(1) ,CX(2) ,ISNX)CX(1)=.5*ALOG(AUX(1))
* CX(2)=0.010=1DO 50 I=2,IEND
I0=10+2IE=IO+1
* PDVT=AUX(IE)PPV=PPVPHA(CX(I0) ,CX(IE) ,ISNX)PHASE=PHAUNW(X,NX,ISNX,I ,PPHASE,PPDVT,PPV,PDVT,ISSUC)
CIF(ISSUC)GO TO 40 0
ISSUC= .PALSE.RETURN
40 PPDVT=PDVTPPHASE=PHASECX(IO)=.5*ALOG(AUX(IO))CX(IE) =PHASE
50 CONTINUE* C
ISFX=(ABS(PHASE/PI)+.1)IF(PHASE.LT.0.0) ISFX=-ISFX
* H-PHASE/FLOAT (NPTS)IE=0DO 60 I=1,IEND
IE-IE+2CX(IE)=CX(IE)-H*FLOAT(I-1)
- .60 CONTINUE
B-20
CCALL FFS(CX,NFFT)RETURN~
END
C SUBROUTINE: SPCVALC SUBROUTINE TO COMPUTRE A SPECTRAL VALUE AT A FREQUENCYC FREQ(RADIANS) FOR SEQUENCE X(N) AND N*X(N)C---------------------------------------------------------------------
CSUBROUTINE SPCVAL(NX,X,FREQ,XR,XI,YRYI)
- DIMENSION X(1)DOUBLE PRECISION UO,Ul,U2,WO,W1,W2,A,B,CD,A1,A2,SAO,CAO
CC
CAO=DBLE (COS (FREQ))SAO=DBLE (SIN (FREQ))Al=2 .D+0*CAOU1=fl.D+0U2=U1WJ1U1W2=Ul
CDO 10 J=1,NX
XJ=DBLE(X(J))UO=XJ+A1 *U1..U2WO=DBLE(FLOAT(J-1)) *XJ+A1*Wl..W2U2=U1Ul=UoW2=W1Wl=Wo
10 CONTINUEC
A=Ul-U2*CAOB=U2*SAOC=Wl-W2*CAOD=W2*SAOA2=DBLE(FREQ*FLOAT(NX~1). -
Ul=DCOS(A2)U2--DSIN (A2)XR=SNGL (U1*A-U2*B)XI=SNGL(U2*A+U1*B)YR=SNGL (Ul*C-U2*D)YI=SNGL (U2*C+U1 *D)RETURNEND
CL -- --------------------------------C FUNCTION: PHAUNWC PHASE UNWRAPPING BASED ON TRIBOLET'S ADAPTIVE INTEGRATION SCHEME.
L B-21I
C THE UNWRAPPED PHASE ESTIMATE IS RETURNED IN PHAUNW.C---------------------------------------------------------------------
- -- - - -- - -C
FUNCTION PHAUNW(X,NX,ISNX,I,PPHASE,PPDVTPPV,PDVT,ISCONS)C --
DIMENSION SDVT(17) ,SPPV(17) ,X(1)INTEGER SINDEX(17) ,PINDEX ISPLOGICAL ISCONS ,FIRSTCOMMON PI,TWOPITHLINCTHLCON,NFFT,NPTS,N,L,H,H1,DVTMN2
C* FIRST=.TRUE.
P INDEX=lsP=1SPPV(SP) =PPVSDVT (SP) =PDVTSINDEX(SP) =L+1
CGO TO 40
C1710 PINDEX=SINDEX(SP)P PHAS E =PHASEPPDVT=SDVT (SP)
* SP=SP-1GO TO 40
C20 IF((SINDEX(SP)-PINDEX) .GT.1)GO TO 30-
ISCONS.FALSEPHAUNW=0.RETURN
C30 K= (SINDEX (SP) +PINDEX) /2
CFREQ=TWOPI*(FLOAT(I-2) *FLOAT(L) .iFLOAT(K-1) )/I1CALL SPCVAL(NX,X,FREQ,XR,XI,YR,YI)
CSP=SP+1SINDEX (SP) =KSPPV(SP) =PPVPHA(XR,XI,ISNX)XMAG=AMODSQ(XR,XI)SDVT(SP) =PHADVT(XRXI ,YR,YI IXHAG)
- C40 DELTA=Hl*FLOAT(SINDEX(SP) -PINDEX)
PHAINC=DELTA*(PPDVT+SDVT(SP))Cto
IF (ABS(PHAINC-DELTA*DVTMN2) .GT.THLINC) GO To 20C
PHASE-PPHASE+PHAINCCALL PHCHCK(PHASE,SPPV(SP) ,ISCONS)IF(.NOT.ISCONS)GO TO 20
CIF(ABS(PHASE-PPHASE) .GT.PI)GO TO 20
B-22
CIF(SP.NE.1)GO TO 10PHAUNW-PHASE0.~RETURNEND
C* C---------------------------------------------------------------------
C FUNCTION: PPVPHAC COMPUTE THE PRINCIPLE VALUE OF THE PHASE OF A SPECTRAL VALUE
V~ ---------------------------------------------------------------------
CFUNCTION PPVPHA(XR,XI ,ISNX)
C tIF(ISNX.EQ..)PPVPHA=(ATAN2( (XI), (XR)))IF(ISNX.EQ.(-1))PPVPHA=(ATAN2(-(XI) ,-(XR)))RETURNEND
rCC FUNCTION: PHADVTC COMPUTE THE PHASE DERIVATIVE OF A SPECTRAL VALUE OF A SEQUENCEX (N)
C---------------------------------------------------------------------
CFUNCTION PHADVT(XR,XI ,YR,YI ,XMAG)
C
PHADVT=-SNGL( (DBLE(XR) *DBLE(YR) +DBLE(XI) *DBLE(YI) )/DBLE(XMAG))RETURNEND
CC---------------------------------------------------------------------
C FUNCTION: AMODSQC COMPUTE THE SQUARE OF THE MODULUS OF A COMPLEX NUMBERC--------------------------------------------------------------------------
CFUNCTION AMODSQ(ZR,ZI)
CANODSQ=SNGL(DBLE(ZR) *DBLE(ZR) +DBLE(ZI) *DBLE(ZI))RETURN
C END
C---------------------------------------------------------------------
C SUBROUTINE: PHCHCKC SUBROUTINE TO CHECK CONSISTENCY OF A PHASE ESTIMATEC---------------------------------------------------------------------
L B-23k
CSUBROUTINE PHCHCK (PH ,PV, ISCONS)
CCOMMON PITWOPITHLINCTHLCON,NFFTNPTS,N,L,HHl,DVTMN2 .LOGICAL ISCONS
CAB= (PH-PV) /TWOPIAl-FLOAT(IFIX (AO))*TOP+PA2mAl+SIGN(TWOPI ,A0)A3=ABS (Al-PH)A4=ABS (A2-PH)
CISCONS=.FALSE.IF(A3.GT.THLCON.AND.A4.GT.THLCON)RETURNISCONS= .TRUE.
CPH=AlIF(A3.GT.A4) PH=A2RETURNEND
CC--------------------------------------------------------------------- 6
*C SUBROUTINE: FFA*C PAST FOURIER ANALYSIS SUBROUTINE
C---------------------------------------------------------------------
C4SUBROUTINE FFA(B, NFFT)
CC THIS SUBROUTINE REPLACES THE REAL VECTOR B(K), (K=1,2.... ,N),C WITH ITS FINITE DISCRETE FOURIER TRANSFORM. THE DC TERM ISC RETURNED IN LOCATION B(l) WITH B(2) SET TO 0. THEREAFTER, THEC JTH HARMONIC IS RETURNED AS A COMPLEX NUMBER STORED ASC B(2*J+1) + I B(2*J+2). NOTE THAT THE N/2 HARMONIC IS RETURNED
*C IN B(N+l) WITH B(N+2) SET TO 0. HENCE, B MUST BE DIMENSIONED*C TO SIZE N+2.
C SUBROUTINE IS CALLED AS FFA (B,N) WHERE N=2**M AND B IS ANC N TERM REAL ARRAY. A REAL-VALUED, RADIX 8 ALGORITHM IS USEDC WITH IN-PLACE REORDERING AND THE TRIG FUNCTIONS ARE COMPUTED ASC NEEDED.C
DIMENSION B(2)COMMON /CON/ PII, P7, P7TWO, C22, S22, P12
CC 1W IS A MACHINE DEPENDENT WRITE DEVICE NUMBERCC 1W =I1MACH(2)
IW=6C
PII = 4.*ATAN(1.)P18 - P11/8. 4P7 =l./SQRT(2.)
B-24
P7TWO =2. *P7C22 - COS (PI18)S22 = SIN(PI8)P12 - 2.*PII .N=DO 10 1=1115M IN N*2IF (N.EQ.NFFT) GO TO 20
10 CONTINUEt WRITE (IW,9999)
9999 FORMAT (30H NFFT NOT A POWER OF 2 FOR FFA)STOP
*20 CONTINUEN8POW = M/3
*C DO A RADIX 2 OR RADIX 4 ITERATION FIRST IF ONE IS REQUIRED* C
IF (M-N8POW*3-1) 50, 40, 30*30 NN=4
INT N/NNCALL R4TR(INT, B(1), B(INT+1), B(2*INT+1), B(3*INT+1)) .GO TO 60
40 NN =.2INT = N/NNCALL R2TR(INT, B(1), B(INT+1))GO TO 60
50 NN=1ICC PERFORM RADIX 8 ITERATIONSC
60 IF (N8POW) 90, 90, 7070 DO 80 IT=1,N8POW
NN = NN*8INT = N/NNCALL RBTR(INT, NN, B(1), B(INT+1), B(2*INT+1), B(3*INT11), -
* B(4*INT+1) , B(5*INT+1) , B(6*INT+1) , B(7*INT+1) , B(1) , -
* B(FT+1) , B(2*INT+1) , B(3*INT+1) , B(4*INT+1) ,. -
B(5INT1)B(6*INT+1), B(7*INT+1))
80 CONTINUECC PERFORM IN-PLACE REORDERING
* C90 CALL ORD1(M, B)
CALL ORD2(M, B)T =B(2)B(2) = 0.B(NFFT+1) = TB(NFFT+2) = 0.
I; DO 100 I=4,NFFT,2B(I) =-B(I)
B-25
100 CONTINUEK RETURN
END
C SUBROUTINE: FFSC FAST FOURIER SYNTHESIS SUBROUTINEC RADIX 8-4-2
C - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
CSUBROUTINE FFS(B, NFFT)
CC THIS SUBROUTINE SYNTHESIZES THE REAL VECTOR B(K), WHEREC K=1,2,.o.N. THE INITIAL FOURIER COEFFICIENTS ARE PLACED INC THE B ARRAY OF SIZE N+i2. THE DC TERM IS IN B(1) WITHC B(2) EQUAL TO 0.C THE JTH HARMONIC IS STORED AS B(2*J+1) + I B(2*J+2).C THE N/2 HARMONIC IS IN B(N+1) WITH B(N+2) EQUAL TO 0.C THE SUBROUTINE IS CALLED AS FFS(B,N) WHERE N=2**M ANDC B IS THE N TERM REAL ARRAY DISCUSSED ABOVE.C
DIMENSION B(2)COMMON /CON1/ PII, P7, P7TWO, C22, S22, P12
* CC IW IS A MACHINE DEPENDENT WRITE DEVICE NUMBERC
*C IW = IIMACH(2)IW= 6
* CPII 4.*ATAN(1.)P18 =PII/8.
P7 I ./SQRT(2.)*P7TWO = 2.*P7
C22 = COS(PI8)S22 = SIN(PI8)P12 =2.*PII
N=DO 10 I=1,15M= IN =N*2
IF (N.EQ.NFFT) GO TO 2010 CONTINUE
WRITE (IW,9999)9999 FORMAT (30H NFFT NOT A POWER OF 2 FOR FFS)
* STOP20 CONTINUE
B(2) = B(NFFT+1)DO 30 I=1,NFFT
B(I) = B(I)/FLOAT(NFFT)30 CONTINUE .
DO 40 I=4,NiFT,2B(I) =-B(I)
B-26
40 CONTINUEN8POW = M/3
CC REORDER THE INPUT FOURIER COEFFICIENTSC
CALL ORD2(M, B)
C CALL ORDI(Ml B)
IF (N8POW.EQ.0) GO TO 60CC PERFORM THE RADIX 8 ITERATIONSC
MN = NDO 50 IT=1,N8POW
INT = N/NCALL RBSYN(INT, NN, B, B(INT+1), B(2*INT+1), B(3*INT+1),
* B(4*INT+1) , B(5*INT+1) , B(6*IMT+1) , B(7*INT+1) , B(1),* B(INT+1) , B(2*INT+1) , B(3*INT+1) , B(4*INT+1),
B(5*INT+1),* B(6*INT+1), B(7*INT+1))NN- M N/B
50 CONTINUEC
*C DO A RADIX 2 OR RADIX 4 ITERATION IF ONE IS REQUIRED* C
60 IF (M-N8POW*3-1) 90, 80, 70
70 INTM= /4CALL R4SYN(INT, B(1), B(INT+1), B(2*INT+1), B(3*INT+1))doGO TO 90
80 INT = N/2CALL R2TR(INT, B(1), B(INT-1))
90 RETURNEND
CC---------------------------------------------------------------------
C SUBROUTINE: R2TR*C RADIX 2 ITERATION SUBROUTINE
C---------------------------------------------------------------------
C0C
SUBROUTINE R2TR(INT, BO, Bi)DIMENSION B0(2), B1(2)DO 10 K=1,IMT
T = B0(K) + B1(K)Bl(K) = B0(K) -Bl(K)
B0(K) = T10 CONTINUE
RETURNEND
CC---------------------------------------------------------------------
B-2 7
C SUBROUTINE: R4TRC RADIX 4 ITERATION SUBROUTINEC---------------------------------------------------------------------
CSUBROUTINE R4TR(INT, BO, Bi, B2, B3)DIMENSION BO(2), B1(2), B2(2), B3(2)
* DO 10 K=1,INTRO = BO(K) +1 B2(K)Rl = B1(K) + B3(K)B2(K) = BO(K) - B2(K)B3(K) = B1(K) - B3(K)BO(K) = RO +I Ri
* Bl(K) = RO Ri10 CONTINUE
RETURNEND
-. CC---------------------------------------------------------------------
C SUBROUTINE: RBTRC RADIX 8 ITERATION SUBROUTINEC---------------------------------------------------------------------
C* SUBROUTINE R8TR(INT, NN, BRO, BRi, BR2, BR3, BR4, BR5, BR6,
BR7,-*BIS, BIl, B12, B13, B14, BIS, B16, B17)
DIMENSION L(15), BR0(2), BR1(2), BR2(2), BR3(2), BR4(2),- . BR5(2),
*BR6(2), BR7(2), BIO(2), BI1(2)r B12(2), B13(2), B14(2),* * B15(2), B16(2), B17(2)
* - COMMON /CON/ PII, P7, P7TWO, C22, S22, P12EQUIVALENCE (L15,L(l)), (L14,L(2)), (L13,L(3)), (L12,L(4)),
* (L11,L(5)), (LiO,L(6)), (L9,L(7)), (L8,L(8)), (L7,L(9)),* (L6,L(10))r (L5,L(11)), (L4,L(12)), (L3,L(13)),
(L2,L(14)),* (Li,L(15))
* CC SET UP COUNTERS SUCH THAT JTHET STEPS THROUGH THE ARGUMENTS
*C OF W, JR STEPS THROUGH STARTING LOCATIONS FOR THE REAL PART OF* . THE
C INTERMEDIATE RESULTS AND JI STEPS THROUGH STARTING LOCATIONS*-C OF THE IMAGINARY PART OF THE INTERMEDIATE RESULTS.C
L(1) = NN18DO 40 K=2,15
IF (L(K-1)-2) 10, 20, 3010 L(K-i) = 220 L(K)= 2
GO TO 4030 L(K) = L(K-1)/240 CONTINUE
PIOVN =PII/FLOAT(NN)
B-28
JI = 3JL = 2JR - 2DO 120 ji=2,Li,2DO 120 J2-Ji,L2,L1Do 120 J3=J2,L3,L2DO 120 J4=J3,L4,L3DO 120 J5=J4,L5,L4DO 120 J6=J5,L6,L5DO 120 J7=J6,L7,L6DO 120 J8=J7,L8,L7Do 120 J9=J8,L9,L8DO 120 J1O=J9,LiO,L9Do 120 Ji1=J10,Li1,L1ODO 120 J12=J11,L12,L11DO 120 J13=J12,L13,L12DO 120 J14=J13,L14,L13DO 120 JTHET=J14,L15,L14
TH2 = JTHET - 2IF (TH2) 50, 50, 90
50 DO 60 K=1,INTTO = BRM + BR4(K)
Tl=BR1(K) +B5KT2 = BR1(K) + BR5(K)T2 = BR2(K) + BR6(K)T4 = BR3(K) - BR7(K)T5 = BR1(K) - BR4(K)T5 = BR1(K) - BR5(K)T7 = BR2(K) - BR6(K)T7 = BR=(TO - T2(KBR2(K) = TO - T2
TO = TO + T2Ti = TI + T3BRO(K = TO + TiBRIMK = TO - TIPR = P7*(T5-T7)PI = P7*(T5+T7) -
BR4(K) = T4 + PRBR7(K) = T6 + PIBR6(K) = T4 - PRBR5(K) = PI - T6
60 CONTINUEIF (NN-8) 120, 120, 70
70 KO =INT*8+ 1KL = KO + INT - 1DO 80 K=KO,KL
PR = P7*(BI2(K)-BI6(K))PI = P7*(B12(K)+B16(K))TRO = BIO(K) + PRTIO - B14(K) + PITR2 - BIO(K) - PRT12 - B14(K) - PIPR = P7*(BI3(K)-BI7(K))PI - P7*(B13(K)+B17(K))
B-29
TRI= BI1 (K) + PRTIl = B15(K) + PITR3 = BII (K) - PRT13 = BI5(K) - PIPR = TR1*C22 - TI1*S22PI = T11*C22 + TR1*S22BI 0(K) = TRO + PRB16 (K) = TRO - PRB17(K) = TIO + PIBI1CK) = PI - TIOPR = -TR3*S22 -T13*C22
* -. PI = TR3*C22 -T13*S22
B12(K) = TR2 + PRB14(K) = TR2 - PRBI5(K) = T12 + PI -
B13(K) = PI - T1280 CONTINUE
GO TO 12090 ARG =TH2*PIOVN
Cl =COS(ARG)
Si SIN(ARG)C2 =Cl**2 - Sl**2S2 =C1*S1 + Cl*SlC3 =C1*C2 - S1*S2S3 =C2*Sl + S2*C1C4 = C2**2 - S2**2S4 = C2*S2 + C2*S2C5 = C2*C3 - S2*S3
*-S5 = C3*S2 + S3*C2C6 = C3**2 - S3**2S6 = C3*S3 + C3*S3
*.C7 = C3*C4 - S3*S4S7 = C4*S3 + S4*C3-INT8 = INT*8JO =JR*INT8 + 1KO =JI*INT8 + 1JLAST = JO + INT -1DO 100 J=J0,JLAST
K = KO + J - JOTRi = BR1(J)*Cl - BII(K)*SlTIl = BR1(J)*S1 + BI1(K)*C1TR2 = BR2(J)*C2 - B12(K)*S2T12 = BR2(j)*S2 + B12(K)*C2TR3 = BR3(J)*C3 - B13(K)*S3T13 = BR3(J)*S3 +- B13(K)*C3TR4 = BR4(J)*C4 - B14(K)*S4T14 = BR4(J)*S4 + B14(K)*C4TR5 = BR5(J)*C5 - B15(K)*S5TI5 = BR5(J)*S5 + B15(K)*C5TR6 = BR6(J)*C6 - B16(K)*S6T16 - BR6(J)*S6 + B16(K)*C6TR7 - BR7(J)*C7 - B17(K)*S7 4_T17 = BR7(J)*S7 + B17(K)*C7
B-30
FcTO BRO(J) + TR4TI= BIO(K) + T14TR4 = BRO(J) - TR4T14 = BIO(K - T14T2 = TRl + TR5T3 = TIl + TI5TR5 =TRi - TR5T15 -TIl T15-T4 =TR2 + TR6T5=T12+ TI6TR6 =TR2 -TR6
TI6 =T12 -TI6
T6 = TR3 + TR7T7 = T13 + T17TR7 = TR3 - TR7T17 = T13 -T17
TR = TO +T4TIO = Ti + T5TR2 = TO - T4
rT12 =TI -T5TRl - T2 + T6TIl = T3 + T7TR3 = T2 - T6T13 = T3 - T7TO = TR4 - T16-Ti = T14 + TR6T4 = TR4 + T16T5 = T14 - TR6T2 = TR5 - TI7T3 = T15 + TR7T6 = TR5 + TI7
*T7 =T15 -TR7*BRO(J) = TRO +- TRI
B17(K) = TIO + TilB16(K) = TRO - TRiBRl(J) = TIl - TIOBR2(J) = TR2 - T13B15(K) = T12 + TR3B14(K) = TR2 + T13
*BR3(J) = TR3 - T12PR = P7*(T2-.T3)PI = P7*(T2.T3)
*.BR4(J) - TO + PRB13(K) - Ti + P!B12(K) - TO - PRBR5(J) = PI - TiPR - -.P7*(T6+T7)PI - P7*(T6..T7).
*BR6(J) - T4 + PRLBI1(K) - T5 + PI
*-BR7(J) - PI - T5
B-3 1LO
100 CONTINUEJR = JR + 2JI - JI - 2 -
IF (JI-JL) 110, 110, 120110 JI - 2*JR -1
JL = JR120 CONTINUE
RETURNEND 2
C -
C---------------------------------------------------------------------
C SUBROUTINE: R4SYNC RADIX 4 SYNTHESISC---------------------------------------------------------------------
CSUBROUTINE R4SYN(INT, BO, Bi, B2, B3)DIMENSION BO(2), B1(2), B2(2), B3(2)DO 10 K=iINT
TO = BOWK + BI(K)TI = BOWK - B1(K)T2 = B2(K) + B2(K)T3 = B3(K) + B3(K)BO(K) = TO + T2B2(K) = TO - T2Bi(K) = TI + T3 _
B3(K) = Ti - T310 CONTINUE
RETURNEND
CC---------------------------------------------------------------------
C SUBROUTINE: R8SYNC RADIX 8 SYNTHESIS SUBROUTINEC---------------------------------------------------------------------
C0- SUBROUTINE R8SYN(INT, NN, BRO, BRi, BR2, BR3, BR4, BR5, BR6,
BR7,* BIO, liI, B12, B13, B14, BI5, B16, B17)
DIMENSION L(15), BRO(2), BRi(2), BR2(2), BR3(2), BR4(2),BR5(2) ,
* BR6(2), BR7(2), BIO(2), BII(2), B12(2), B13(2), B14(2),* BI5(2), B16(2), B17(2)
COMMON /CONI/ PII, P7, P7TWO, C22, S22, P12EQUIVALENCE (Li5,L(i)), (Li4,L(2)), (L13,L(3)), (Li2,L(4)),
* (L11,L(5)), (Ll0,L(6)), (L9,L(7)), (L8,L(8)), (L7,L(9)),(L2,LL(i4)), (L5,L(1i)), (L4,L(i2)), (L3,L(i3)),
L(l) = NN/8DO 40 K=2,15
4 B-32
IF (L(K-1)-2) 10, 20, 301e L(K-1) ='220 L(K) 2 .
GO TO 4030 L(K) =L(K-1)/2
40 CONTINUE
PIOVN = PII/FLOAT(NN)
JL = 2JR =2
CDO 120 J1=2,L1,2DO 120 J2=J1,L2,L1DO 120 J3=J2,L3,L2DO 120 J4=J3,L4,L3DO 120 J5=J4,L5,L4DO 120 J6=J5,L6,L5DO 120 J7=J6,L7,L6DO 120 J8=J7,L8,L7DO 120 J9=J8,L9,L8
FDO 120 J1O=J9,L10,L9-DO 120 J11=J10,L11,L1ODO 120 J12=J11,L12,L11DO 120 J13=J12,L13,L12DO 120 J14=J13,L14,L13DO 120 JTHET=J14,L15,L14
TH2 = JTHET - 2p IF (TH2) 50, 50, 9050 DO 60 K=1,INT
TO = BRO(K +4 BR1(K)Ti = BRO(K) - BR1(K)T2 = BR2(K) +BR2(K)T3 = BR3(K) + BR3(K)
PT4 = BR4(K) +- BR6(K) ~T6 = BR7(K) - BR5(K)T5 - BR4(K) - BR6(K)T7 = BR7(K) + BR5(K)PR = P7*(T7+T5)PI = P7*(T7-T5)
-TTO =TO +T2MT -Ti + T3T2 =TO - T2 -T3 =TI - T3T4 =T4 + T4T5 =PR + PRT6 =T6 + T6T7 -PI+ PIBROWK TTO + T4BR1(K) -TT1 + T5BR2(K) -T2 + T6BR3(K) -T3 + T7BR4(K) - TTO - T4BR5(K) = TT1 - T5
B-3 3
BR6(K) -T2 -T6
BR7(K) =T3 -T7
60 CONTINUE-IF (NN-8) 120, 120, 70
*70 KO=-INT*8+i1KL=-KO +INT-i1DO 80 K=K0,KL
TI - B10(K) + B16(K)T2 - B17(K) - B11(K) ~T3 - BIO(K - BI6(K)T4 - B17(K) + BI1(K)
*-PR = T3*C22 + T4*S22*PI = T4*C22 - T3*S22
T5 = B12(K) + B14(K)T6 = B15(K) B 13(K)T7 = B12(K) B 14(K)T8 = B15(K) + B13(K)RR = T8*C22 - T7*S22RI = -T8*S22 - T7*C22B10(K) - (T1+T5) + (T1+T5)B14(K) = (T2+T6) + (T2+T6)BIi(K) = (PR+RR) + (PR+RR)B15(K) = (PI+RI) + (PI+RI)T5 = Ti - T5T6 = T2 - T6B12(K) = P7TWqO*(T6+T5)BI6(K) = P7TWO*(T6-TS)5RR = PR - RR......RI = PI - R IB13(K) = P7TWO*(RI+RR)B17(K) = P7TWO*(RI-RR)
*80 CONTINUEGO TO 120
9 ARG = TH2*PIOVN
Ci = COS(ARG)Si = -SIN(ARG)C2 = Cl**2 - Si**2S '~ 2 = Ci*Si + C1*SlC3 = Ci*C2 - Si*S2S3 = C2*Si + S2*CiC4 = C2**2 - S2**2S4 =C2*S2 + C2*S2
* S=C2*C3 - S2*S3CC -5= C3*S2 + S3*C2C6 =C3**2 - S3**2S6 =C3*S3 + C3*S3C7 =C3*C4 - S3*S4S7 =C4*S3 + S4*C3INT8 = INT*8. -
JO = JR*INT8 + 1KO - JI*INT8 + 1JLAST =JO + INT 1 4
*DO 100 J=JO,JLAST
B-34
K =KO + J -JO
TRI = BRO (J) - B16 (K)TII = B17 (K) + BR1 (J) -
TRi = BR2 (J) + BI14(K)T12 = BI75KW - BRi (J)TR2 BI25JM + B14 (K)T13 = BI 4(K) - BR3 (J)
TR4 = BR4 (J) + B12(K)T14 = B13(KW - BR5 (J)TO = BR4(J) - B12(K)Ti = B13(K) + BR5(J)TR5 = P7*(TO+Ti)T15 = P7*(Ti .TSTR6 = BR6(J) + BIO(K) .0T16 = BII(K) -BR7(J)
TO = BR6(J) -BIO(K)
Ti = BII(K) + BR7(J)TR7 = -P7*(TO-Tl)T17 = -.P7*(Ti+TO)TO =TR + TR2 .Ti = TIO + T12T2 = TRl + TR3T3 =TII + T13TR2 =TRO TR2T12 =TIO T123 TR3 =TRI- TR3T13 =TIl T13T4 =TR4 + TR6T5 =T14 + T16T6 =TR5 + TR7T7 =T15 + T17
* TTR6 =T14 -T16T16 =TR6 - TR4TTR7 = T15 - T17T17 =TR7 - TR5BRO(J) = TO + T4BIO(K) = Ti + T5BRI(J) = Cl*(T2+T6) -Sl*(T3+T7)
BII(K) = Ci*(T3+T7) 4+ Si*(T2+T6)BR2(J) = C2*(TR2+TTR6) -S2*(TI2+TI6)
B12(K) = C2*(T12.4T16) + S2*(TR24TTR6)BR3(J) = C3*(TR34.TTR7) -S3*(TI3+TI7)
B13(K) = C3*(TI3+iTI7) 4- S3*(TR3+TTR7)BR4(J) = C4*(TO-T4) - S4*(TI-T5)B14(K) = C4*(Ti-T5) + S4*(TO-T4)BR5(J) = C5*(T2-T6) - S5*(T3-T7)B15(K) = C5*(T3-T7) + S5*(T2-T6)BR6(J) = C6*(TR2-TTR6) - S6*(TI2-TI6)B16(K) - C6*(TI2-TI6) + S6*(TR2-TTR6)BR7(J) = C7*(TR3-TTR7) - S7*(TI3-TI7)B17(K) = C7*(TI3-TI7) + S7*(TR3-TTR7)
B-35
100 CONTINUEJR = JR + 2JI - JI - 2IF (JI-JL) 110, 110, 120
110 JI=-2*JR -1JL - JR
120 CONTINUERETURN
END
C SUBROUTINE: ORDIC IN-PLACE REORDERING SUBROUTINEC---------------------------------------------------------------------s--
SUBROUTINE ORD1(M, B)DIMENSION B(2)
CK 4KL =2LN =2**M
DO 40 J=4,N,2IF (K-J) 20, 20, 10
10 T =B(J)B(J) = B(K)B(K) = T
20 K =K -2IF (K-KL) 30, 30, 40
30 K =2*JKL = J
40 CONTINUERETURNEND
CC---------------------------------------------------------------------
C SUBROUTINE: ORD2C IN-PLACE REORDERING SUBROUTINE_C---------------------------------------------------------------------
CSUBROUTINE 0RD2(M, B)DIMENSION L(15), B(2)EQUIVALENCE (L15,L(l)), (L14,L(2)), (L13,L(3)), (L12,L(4)),
* (Lll,L(5)), (L1O,L(6)), (L9,L(7)), (L8,L(8)), (L7,L(9)),* (L6,L(10)), (L5,L(11)), (L4,L(12)), (L3,L(13)),
(L2,L(14)),* (L1,L(15))
N - 2**ML(1) - NDO 10 K=2,M
L(K) =L(K-1)/2
B-36
.: .
10 CONTINUEDO 20 K-M,14
L(K+1) - 2* 20 CONTINUE*IJ - 2
DO 40 Jl-2,Ll,2DO 40 J2=J1,L2,LlDO 40 J3-J2,L3,L2DO 40 J4-J3,L4,L3DO 40 J5-J4,L5,L4DO 40 J6=J5,L6,L5DO 40 J7-J6,L7,L6DO 40 J8-J7,L8,L7DO 40 J9=J8,L9,L8DO 40 J1O=J9?L1O,L9DO 40 Jll=JlO,Ll1,LlODO 40 J12=J11,L12,LllDO 40 J13=J12,L13,L12DO 40 J14=J13,Ll4,L13DO 40 JI=J14,Ll5,L14
30 IF (IJ-JI) 30, 40, 4030 T = B(IJ-1)
B(IJ-1) = B(JI-1)B(JI-1) = TT = B(IJ)B(IJ) = B(JI)B(JI) = T
40 IJ =IJ+ 2RETURNEND
CC---------------------------------------------------------------------
pC SUBROUTINE: FFT842*C FAST FOURIER TRANSFORM FOR N=2**M
C COMPLEX INPUTC---------------------------------------------------------------------
* CSUBROUTINE FFT842(IN, N, X, Y)
CC THIS PROGRAM REPLACES THE VECTOR Z=X+IY BY ITS FINITEC DISCRETE, COMPLEX FOURIER TRANSFORM IF IN=0. THE INVERSE
* TRANSFORMC IS CALCULATED FOR IN=l. IT PERFORMS AS MANY BASEC 8 ITERATIONS AS POSSIBLE AND THEN FINISHES WITH A BASE 4ITERATION
C OR A BASE 2 ITERATION IF NEEDED.CC THE SUBROUTINE IS CALLED AS SUBROUTINE FFT842 (IN,N,X,Y).C THE INTEGER N (A POWER OF 2), THE N REAL LOCATION ARRAY X, AND
C THE N REAL LOCATION ARRAY Y MUST BE SUPPLIED TO THE SUBROUTINE.
B-37
CDIMENSION X(2), Y(2), L(15)COMMON /CON2/ P12, P7EQUIVALENCE (L15,L(1)), (L14,L(2)), (L13,L(3)), (L12,L(4)),
* (L11,L(5)), (L10,L(6)), (L9,L(7)), (L8,L(8)), (L7,L(9)),* (L6,L(10)), (L5,L(11)), (L4,L(12)), (L3,L(13)),
(L2,L(14)),* (L1,L(15))
CC -
C IW IS A MACHINE DEPENDENT WRITE DEVICE NUMBER* C
C IW = I1MACH(2)IW= 6
P12 =8.*ATAN(1.)P7 l ./SQRT(2.)DO 10 I=1,15M= INT =2**1
IF (N.EQ.NT) GO TO 20 --
10 CONTINUEWRITE (IW,9999)
*9999 FORMAT (35H N IS NOT A POWER OF TWO FOR FFT842)STOP
20 N2POW = MNTHPO = N-
I FN = NTHPOIF (IN.EQ.1) GO TO 40DO 30 I=1,NTHPO
Y(I) =-Y(I)
30 CONTINUE40N8POW = N2POW/340IF (N8POW.EQ.0) GO TO 60
CC RADIX 8 PASSES,IF ANY.
* CDO 50 IPASS=1,N8POW
NXTLT = 2**(N2POW-3*IPASS)LENGT = 8*NXTLTCALL R8TX(NXTLT, NTHPO, LENGT, X(1), X(NXTLT+1),
X(2*NXTLT+1),*X(3*NXTLT+1), X(4*NXTLT+1), X(5*NXTLT+1), X(6*NXTLT+1),*X(7*NXTLT+1), Y(1), Y(NXTLT+1), Y(2*NXTLT+1),
Y(3*NXTLT+1) -
*Y(4*NXTLT+1), Y(5*NXTLT+1), Y(6*NXTLT+1), Y(7*NXTLT+1))50 CONTINUE
* C*C IS THERE A FOUR FACTOR LEFT
C60 IF (N2POW-3*N8POW-1) 90, 70, 80
C*C GO THROUGH THE BASE 2 ITERATION
B-3 8
rCC
70 CALL R2TX(NTHPO, X(1), X(2), Y(l), Y(2))
GOGO TO 90
C OTHROUGH THE BASE 4 ITERATIONC
* ~80 CALL R4TX(NTHPO, X(1), X(2), X(3), X(4), Y(1), Y(2), Y(3), t-
90 DO 110 J=1,15L(J) 1IF (J-N2POW) 100, 100, 110
100 L(J) = 2**(N2POW+I-J)-110 CONTINUE
IJ =1 IDO 130 J1=1,L1DO 130 J2=J1,L2,L1DO 130 J3=J2,L3,L2DO 130 J4=J3,L4,L3DO 130 J5=J4,L5,L4
rDO 130 J6=J5,L6,L5DO 130 J7=J6,L7,L6DO 130 JB=J7,L8,L7DO 130 J9=J8,L9,L8DO 130 J1O=J9,L1O,L9DO 130 J11=J10,L11,L10KDO 130 J12=J11,L12,L11DO 130 J13=J12,L13,L12DO 130 J14=J13,L14,L13DO 130 JI=J14,L15,L14
IF (IJ-JI) 120, 130, 130120 R = X(IJ)
* X(IJ) =X(JI)
X(JI) =R
FI = Y(IJ)Y(IJ) = Y(Ji)Y(JI) = FI
130 1J= iJ+1IIF (IN.EQ.1) GO TO 150DO 140 I=1,NTHPO
Y(I) = -Y(I)140 CONTINUE
GO TO 170150 DO 160 I=1,NTHPO
- X(I) = X(I)/FNY(I) = Y(I)/PN
160 CONTINUE170 RETURN
ENDC
C------------------------------------------------------------------------- S
B-39
C SUBROUTINE: R2TXC RADIX 2 ITERATION SUBROUTINEC---------------------------------------------------------------------
SUBROUTINE R2TX(NTHPO, CR0, CR1, CIO, Cl)DIMENSION CR0(2), CR1(2), CIO(2), CI1(2)DO 10 K=1,NTHPO,2
RI = CRO(K) +- CR1(K)CR1(K) = CRO(K) - CRI(K)CRO(K) = RIF11 = CIO(K) + CI1(K)CI1(K) = CIO(K) - CII(K)CIO(K) = FIl
10 CONTINUERETURNEND
CC---------------------------------------------------------------------
C SUBROUTINE: R4TXC RADIX 4 ITERATION SUBROUTINEC---------------------------------------------------------------------
CSUBROUTINE R4TX(NTHPO, CR0, CR1, CR2, CR3, CIO, ClI, C12,
C13)DIMENSION CRO(2), CR1(2), CR2(2), CR3(2), CIO(2), CI1(2), .
C12(2),* C13(2)
DO 10 K=1,NTHPO,4* RI = CR0(K) + CR2(K)
R2 = CRO(K) - CR2(K)R3 = CR1(K + CR3(K)R4 = CR1(K) -CR3(K)
F11 = CI0(K) + C12(K)F12 = CIO(K) - C12(K)F 13 = CI1(K) +i C13(K)F14 = CI1(K) - C13(K)CRO(K) = Ri + R3CIO(K) = F11 + F13CR1(K) = Ri R3CI1(K) = F11 F 13
*CR2(K) = R2 F 14C12(K) = F12 + R4CR3(K) = R2 + 14C13(K) = F12 -R4
10 CONTINUERETURN
-. - ENDCC------------------------------------------------------------------------q_
B-40
C SUBROUTINE: R8TXC RADIX 8 ITERATION SUBROUTINEC---------------------------------------------------------------------
CSUBROUTINE R8TX(NXTLT, NTHPO, LENGT, CR0, CR1, CR2, CR3, CR4,
* CR5, CR6, CR7, CIO, ClI, C12, C13, C14, CI5, C16, C17)DIMENSION CRO(2), CRl(2), CR2(2), CR3(2), CR4(2), CRS(2),
CR6(2),- * CR7(2), CIi(2), C12(2), C13(2), C14(2), CI5(2), C16(2),
* C17(2), CIO(2)COMMON /CON2/ P12, P7
CSCALE = P12/FLOAT(LENGT)DO 30 J=1,NXTLTARG =FLOAT(J-1)*SCALECi COS(ARG)Si SIN(ARG)C2 =Ci**2 - Sl**2S2 =C1*Si + Ci*SiC3 =Cl*C2 - S1*52S3 =C2*Si + S2*C1C4 =C2**2 - S2**2S4 =C2*S2 + C2*S2C5 = C2*C3 - S2*S3S5 = C3*S2 + S3*C2C6 = C3**2 - S3**2S6 = C3*S3 + C3*S3-C7 = C3*C4 -..53*S4S7 = C4*S3 + S4*C3DO 20 K=J,NTHPO,LENGT
ARO = CRO(K) + CR4(K)AR1 = CR1(K) + CR5(K)
*AR2 = CR2(K) + CR6(K)AR3 = CR3(K) + CR7(K)AR4 = CRO(K) - CR4(K)AR5 = CRI(K) - CR5(K)AR6 = CR2(K) - CR6(F4AR? = CR3(K) - CR7(K)AIO =CI0(K) + C14(K)All = Ci(K) + C15(K)A12 = C12(K) + C16(K)A13 = C13(K) + C17(K)A14 = CIO(K) - C14(K)AI5 w CII(K) - CIS(K)A16 =C12(K) - C16(K)A17 = C13(K) - C17(K)BR0 = ARO + AR2BRi = ARI + AR3BR2 = AR0 - AR2BR3 = ARI - AR3
(BR4 = AR4 - A16BR5 = AR5 - A17BR6 = AR4 + A16 - .-
B-4 1
BR7 = AR5 + A17BIO = AIO + A12BIl = All + A13B12 =AI - A12B13 - All - A13B14 = A14 + AR6B15 = AI5 + AR7B16 = AI4 - AR6BI7 = A15 - AR7CRO(K) = BRO + BRiC10(K) = BIB + BIlIF (J.LE.l) GO TO 10CRl(K) = C4*(BRO-BR1) -S4*(BIO-BIl)
CIl(K) = C4*(BIO-BIl) +- S4*(BRO-BR1)CR2(K) = C2*(BR2-BI3) - S2*(BI24-BR3)C12(K) = C2*(B12+BR3) +i S2*(BR2-BI3)CR3(K) = C6*(BR2+B13) - S6*(B12-BR3)C13(K) = C6*(B12-BR3) + S6*(BR2+B13)
* TR = P7*(BRS-BI5)TI = P7*(BR5+BI5)CR4(K) = Cl*(BR4ITR) - Sl*(B14+TI)-C14(K) = Cl*(B14+TI) + S1*(BR4+TR)CR5(K) = C5*(BR4-TR) - S5*(BI4-TI)C15(K) = C5*(B14-TI) +- S5*(BR4-TR)TR = -P7*(BR7+BI7)TI = P7*(BR7-BI7)CR6(K) = C3*(BR6+TR) - S3*(BI6+TI)-CIE(K) = C3*(BI6+TI) + S3*(BR6+TR)CR7(K) = C7*(BR6-TR) - S7*(BI6-TI)C17(K) = C7*(BI6-.TI) +- S7*(BR6-TR)GOTO20
10 CRl(K) = BRO - BRICI1(K) = BIB - BIlCR2(K) = BR2 - B13C12(K) = B12 + BR3CR3(K) = BR2 + B13C13(K) = B12 - BR3
* . TR = P7*(BRS-BI5)TI = P7*(BR5+BI5)CR4(K) = BR4 + TRC14(K) = B14 + TICR5(K) =BR4 -TRC15(K) =B14 -TITR = ...P7*(BR7+BI7)TI = P7*(BR7-BI7)-CR6(K) = BR6 + TRC16(K) = B16 + TICR7(K) = BR6 - TRC17(K) = BI6 - TI
20 CONTINUE30 CONTINUE
RETURN* * END
B-42
CCXTRA.FOR
SUBROUTINE RP(XYRtTH,N,ID)C REC - POLAR CONVERSION :
C ID NOT =1 =>R->PC ID =1 ==> P->R
REAL*8 X(16384) ,Y(16384) ,R(16384) ,TH(16384)0REAL*8 DSQRTDATAN2,DCOSDSINIF(ID.EQ.1)GO TO 10DO 5 I=1,NR(I)=DSQRT(X(I) *X(I)+Y(I) *Y(I))TH(I)=0.DOIF(Y(I).EQ.0.DO.AND.X(I).EQ.0.DO)GO TO 5aTH(I)=DATAN2(Y(I) ,X(I))
5 CONTINUERETURN
10 CONTINUEDO 15 I=1,NX(I) =R(I) *DCOS(TH(I))p
15 Y(I)=R(I)*DSIN(TH(I))RETURNEND
CCC
SUBROUTINE MR1DF (LOG2N,X,Y,SIGN)C FORTRAN VERSIONC MIXED RADIX FOURIER TRANSFORM
INTEGER LOG2N ..
REAL*8 X(16384) ,Y(16384)p DIMENSION 5(13) ,U(13)
CINTEGER J1,J2,J3,J4,JT,NM4REAL*8 ARGClC2,C3,51 ,S2,S3,Rl,R2,R3,R4,R5,R6,R7,R8,TREAL*8 DCOS,DSIN
C. -
C .C
INTEGER ABrCDEF,G,H,I,J,KL,M,1 BS,CS,DS,ES,FSGS,HS,IS,JS,KS,LS,MS,2 AL,BL,CL,DL,EL,FL,GL,HL,ILJL,KL,ML,S,U
EQUIVALENCE(BSS(2)),(CS,S(3)),(DS,S(4)),(ES,S(5)),(FS,S(6)),
1(GS,S(7)) ,(HS,S(8)) ,(ISS(9)) ,(JSS(10) ) ,(KS,S(11)) ,(LS,S(12))t
2(MS,S(13)) ,(AL,U(1)) ,(BL,U(2)) ,(CL,U(3)) ,(DL,U(4)) ,(EL,U(5)),
3(PL,U(6)) ,(GL,U(7)) ,(HL,U(8)) ,(IL,U(9)) ,(JL,U(10)) ,(KL,U(11)) l b
4 (LL,U(12)),(MLU(13))
B-43
CN=2* *LO2NIF (SIGN) 800,p8690,8002-
8000 DO 8001 I=1,N8001 Y(I)=-Y(I)8002 CONTINUE
IF (LOG2N-1) 509,500,501501 CONTINUE
Do 400 K=2,LOG2N,2M=2** (LOG2N-K) -
Mh4-4*MDO 300 J=1,M
ARG=6.28315D0*DBLE(FLOAT(J-1)/FLOAT(M4))C1=DCOS (ARG)S1=DSIN (ARG)C2=C1*C1-Sl*SlS2=Cl*S1+Cl*SlC3-C2*Cl-S2*S1S3=C2*S1+S2*C1DO 200 I=t44,NM4J1=I+J-M4J2=Jl+MJ3=J2+MJ4=J3+MbR1=X(J1) +X(J3)R2=X(J1) -X(J3)R3=Y(J1) +Y(J3)- -
R4=Y(J1) -Y(J3)4R5=X(J2) +X(J4)R6-X (J2) -X (J4)R7 =Y(J 2) +Y (J 4)R8=Y(J2) -Y(J4)X(J1) =R1+R5Y(J1) =R3+R7
IF(ARG) 101,100,101101 CONTINUE
X(J3) =(R2+R8) *C1+(R4.-R6) *SlY(J3)=(R4-R6)*Cl-(R2+R8)*SlX(J2)=(R1-R5)*C2+(R3-R7)*S2Y(j2)=(R3-R7)*C2-(R1-R5)*S2X(J4) =(R2-R8) *C3+(R4+R6) *S3-Y(J4)=(R4+R6)*C3-(R2-R8)*S3GO TO 200
100 CONTINUEX(J3) =R2+R8Y(J3) =R4-R6X (J2) =R1-R5Y(J2) =R3-R7X(J4) =R2-R8Y(J4) =R4+R6
200 CONTINUE-300 CONTINUE
400 CONTINUE
B-44
500 CONTINUEITEST LOG2N- (LOG2N/2*2)
IF(ITEST) 701,700,701701 CONTINUE
DO 600 I-1,N,2RlmX(I) +X(I+1)
R3=Y(I)+Y(I+l) *.
R4-Y(I) -Y(I+1)
- Y(I)-R3X(I+1) mR2Y(I+1)-R4
600 CONTINUE700 CONTINUE
MS-N/2!4L-NDO 800 K=2,12J=14-K5(J) =1U(J)=S(J+1)
r IF(S(J+1) -1) 7701,7701,7700 .
7700 S(J)=S(J+1)/27701 CONTINUE800 CONTINUE
AL-BSJT= 0
* DO 900 A=1,ALDO 900 B=A,BL,BSDO 900 C=B,CL,CSDO 900 D=C,DL,DSDO 900 E=D,EL,ES
DO 900 F=E,FLFSDO 900 G=FGLGSDO 900 H=G,HL,HSDO 900 I=H,IL,ISDO 900 J=IJL,JSDO 900 K=J,KLKSDO 900 L=K,LL,LSDO 900 M=L,ML,MS
- JT-JT+lIF(JT-4) 900,900,901
901 CONTINUET=X(JT)X(JT)-X(M)X(M) =T
9.
T=Y(JT)Y(JT) =Y(M)Y(h) =T
900 CONTINUERETURNEND
B-45
-... .,-.* .--- --.-. .~ -
SHIFTF.FOR
SUBROUTINE SHIFTF(F,N)coo.C... SHIFTS PHASE OF ARRAY SO THAT ANGLE OF FIRST ELEMENT ISZERO
C.o.C... GIVEN THE FIRST ELEMENT a+ib AND ANY ELEMENT X+iYcoo*C.00C.00C.o. * *
*
C..o sqrt(a**2+b**2) * * *
C... * *b and **Y*C... * * * -, -.- ,
C*f
C... * angle * * ANGLE
*C... ******************** **********
C.. a XCo. ..-C.. SHIFT THE PHASE BY angle*C... * , :/C... ,'* *'..C.00 *
C... * *Yl -C.. ANGLE-angle *
C ... Xl..%
C. ..C.. •SIN(angle)=b/sqrt(a**2+b**2)C.o. COS(angle) =a/sqrt(a**2+b**2)
C... I Xl I I COS(angle) SIN(sngle)l I X IC... I I -1 I I I .-:
cSUC I Yl I I-SIN(angle) COS(angle) l I Y IC... SUCH THAT:C... Xl= [a/sqrt(a**2+b**2)]*X + [b/sqrt(a**2+b**2)]*YC... Yl--[b/sqrt(a**2+b**2)]*X + [a/sqrt(a**2+b**2)]*Y
*C.... . ._ -
DIMENSION F(l)
A-F(l) --
B-F(2)
B-46
.w-
-' ..-,
.: * * ". .. .*: * *.' : ' ": -, ; : ::.:...'.:':..-. . ..,:.'',:... . . . . . .. . ... ... .:.. . . . . . .::.. . . . . . . . . . . . . . . . . ..:.:. .."'. . ."'" ::?':'"2: ,'
AKUL=A/SRT(**2+**2
BKULT=A/SQRT (A**2+B**2)
DO 100 I-1,N+2,2X=F(I)Y=F(I+1)F (I)=AKULT*X+BMULT*YF (1+1) =-BKULT*X+AI4ULT*Y
100 CONTINUERETURN
END
B-47
Appendix C
PATTERN RECOGNITION
* SCATTER PLOT PRODUCTION
"i- p-:."-
Appendix C
P PATTERN RECOGNITION SCATTER PLOT PRODUCTION
Start with several sampled data files that represent the data from which patternsimilarities are to be extracted. Each segment of data to be analyzed is labeled. Labelfiles must be created with the ILS command $ LBF 0, which is similar to the manner
I ~ in which sampled data files are created with the $ FIL 0 command as in this example.Use of a command file is suggested when many label files are to be created.
To label the segments, use ILS command $ LBA. Data segments must have beenpreviously selected by use of one of the ILS commands $ DSP or $ CUR so that this
-- information is in the user's common file. A label file contains a series of labels, eachone of which is a two-line record of ASCII characters that describes a segment of in-terest in a sampled data file. Next, use ILS command $ OUR to extract signal features.Because ILS command $ OUR restricts the user to 32 frequency spectra, a local versionwas used that selects 32 evenly spaced spectra from the output of a 2048-point FFT.To use OUR (or XUR), first designate the label file that contains pointers to the area of
r interest in the signal. $ OUR output will be in the form of feature record files. W,-
Using ILS command $ SME, create output feature record files which contain meanvector and eigen records. Since $ SME is now restricted to 20 elements in analysis,
. first extract the 20 most significant elements in the output records using ILS command$ MRE. Use the same elements for all records analyzed. If you have used OUR on sin-gle data samples, collect the samples in two or more record files using $ TRE for analy-sis with $ SME. In this study, ILS command $ SME 6 was used. One output record fileis produced by $ SME containing the mean and eigen vector records. Next, using thefiles input to $ SME and the output file of $ SME, perform a principal component anal-
-.. ysis of those input files. $ PCO outputs a record file for each input file. Plot the results
with $ PLR.
UI Examples are given on the following pages.
C,-
:::
K: C_.
Example:Ten sampled data files exist which are numbered 1405 through 1495in steps of 10.Create the label file(s).$ LBF 0 <cr>OPTIONS TO MANIPULATE LABEL FILES:ENTER FILENAME [,DKI TO SELECT A FILEENTER C <RETURN> TO CREATE A FILE - .ENTER I <RETURN> TO SET THE INITIALSENTER <RETURN> TO EXIT->C :~ENTER FILENAME [,DK]
->TAM1DRBO:[ILSMGR.DGN]TAMl.LAB LABEL DATA
0 LABELS, INITIALS: - - /.PRIMARY LABEL FILE
OPTIONS TO MANIPULATE LABEL FILES:ENTER FILENAME [,DK] TO SELECT A FILEENTER C <RETURN> TO CREATE A FILEENTER I <RETURN> TO SET THE INITIALS -
ENTER <RETURN> TO EXIT->IENTER THE INITIALS
->TAMDRBO:[ILSMGR.DGN]TEST2.LAB LABEL DATA
0 LABELS, INITIALS: TAM "PRIMARY LABEL FILE -
OPTIONS TO MANIPULATE LABEL FILES:ENTER FILENAME [,DKI TO SELECT A FILEENTER C <RETURN> TO CREATE A FILEENTER I <RETURN> TO SET THE INITIALSENTER <RETURN> TO EXIT -
-><cr> ".In like manner create the other nine label files.
Use of a command file is suggested when many label files are tobe created.
Label the segments, having previously indicated the range by thecursor command or by the $ DSP range.Point to the label file by issuing the command $ LBF TAM1.DRBO:[ILSMGR.ILS]TAMI.LAB LABEL DATA
1 LABELS, INITIALS: "PRIMARY LABEL FILE$ LBA
FIELD-1 IS OBTAINED FROM THE FILE HEADER, @=ABORTENTER FIELD-2;FIELD-3;FIELD-4;FIELD-5;FIELD-6
->TAMTESTList the label file$ LLADRB0:[ILSMGR.ILS]TAMl.LAB 22-MAY-84 PAGE 1 ''
C-2 "
% ., ......-.-. .. ... ,..... .. ... . -... ... .- .. a '. ..- j.-. •.,' ..... °.. "
* *****LABEL 1*************************TAMTEST ; ; ; -.1; 1; 1;2048; 2080;DRAO:[ILSMGR.ILS]WD1405. ;27-JAN-84;TAM
Label the rest of the files.Extract the features$ XURENTER MODE, EXTRACTION CODE AND NUMBER OF FEATURESMODE: M MEAN FRAMES
C = CONSECUTIVE FRAMESFEATURE: 1 AUTOREGRESSIVE COEFFICIENTS
2 - REFLECTION COEFFICIENTS3 = AUTOCORRELATION COEFFICIENTS4 FREQUENCY SPECTRA5 = LP CEPSTRAL COEFFICIENTS6 - MEL CEPSTRAL COEFFICIENTS7 RESONANCE FREQ AND BAND (PEAK PICK)8 = RESONANCE FREQ AND BAND (ROOT SOLVE)9 - NORMALIZED RESONANCE FREQ AND BAND (ROOT SOLVE)
- >4EXTRACTION CODE = 4
USING LABEL FILE .... DRBO:[ILSMGR.ILS]TXMI.LABUSING RECORD FILE .... DRBO:[ILSMGR.ILS]WD1000. .LEVEL 1FIELD-1 IS OBTAINED FROM THE FILE HEADER, @=ABORTENTER FIELD-2;FIELD-3;FIELD-4;FIELD-5;FIELD-6 FOR SEARCHENTER <RETURN> TO START SEARCH
SDRB:[ILSMGR.ILS]WDI0, RECORD 1 STOREDAnd so on with the rest of the files.Using $ MRE move the first twenty elements in each fileto another file$ MREMOVE FEATURE RECORDS FROM A FILE AND
* EXTRACT SELECTED ITEMS AND ELEMENTS FROM RECORDS
" ENTER.,,ELEMENT NUMBER(S) TO EXTRACT FROM EACH ITEMUSE <ALL> <RETURN> FOR ALL ELEMENTSUSE <F> <RETURN> TO FINISHUSE <A> <RETURN> TO ABORTMAXIMUM OF 12 ENTRIES/LINE, NEGATIVE IMPLIES INCLUSIVE
->1,-20->FENTER...ITEM NUMBER(S) TO EXTRACT FROM EACH RECORD
USE <ALL> <RETURN> FOR ALL ITEMSUSE <F> <RETURN> TO FINISH -USE <A> <RETURN> TO ABORTMAXIMUM OF 12 ENTRIES/LINE, NEGATIVE IMPLIES INCLUSIVE
->ALLENTER ... RECORD NUMBER(S) OF EACH RECORD TO TRANSFER
USE <ALL> <RETURN> FOR ALL RECORDS1. USE <F> <RETURN> TO FINISH . -
USE <T> <RETURN> TO TEST O ELF:1ENTS (MAX=10)USE <SK> NO. PEC <RETUPI TO SKIP RECORDS
C-3V ' J,
71 = - ' . V - --
USE <AV> NO. REC <RETURN> TO AVERAGE RECORDSUSE <AVI> NO. REC <RETURN> TO AVERAGE ITEMS IN RECORDS
iUSE (A> <RETURN> TO ABORTMAXIMUM OF 12 ENTRIES/LINE, NEGATIVE IMPLIES INCLUSIVE
->ALL*ENTER...FILE NO., DISK NO. OF INPUT FILE
->1010ENTER...FILE NO., DISK NO. OF OUTPUT FILE
->1021DRB0: [ILSMGR.ILS]WD1021. RECORD 1 STORED
And so on with the rest of the files.*Collect the records in two files for analysis.
$ FIL 1021*DRBO:[ILSMGR.ILS]WD1021. RECORD DATA
12 DK BLKS, 1 RECORDSPRIMARY FILE
$ FIL S1031DRBO:[ILSMGR.ILS]WD1031. DOES NOT EXIST
* SECONDARY FILE$ OPN S2$ TRE 1,1,5,1,2,5USING DRB0:[ILSMGR.ILS]WD1021.
*DRBO:[ILSMGR.ILSIWD1031. RECORD 1 STOREDUSING DRBO:[ILSMGR.ILS]WD1022.DRBO:[ILSMGR.ILS]WD1031. RECORD 2 STOREDUSING DRBO:(ILSMGR.ILS]WD1023.DRB0:IILSMGR.ILS]WD1031. RECORD 3 STOREDUSING DRB0: (ILSMGR.ILSIWDl024.DRB0: (ILSMGR.ILS]WD1031. RECORD 4 STORED
* USING DRBO:[ILSMGR.ILS]WD1025.DRB0:[ILSMGR.ILS]WD1031. RECORD 5 STOREDUSING DRBO:[ILSMGR.ILS]WD1026.DRB0: [ILSMGR.ILS]WD1032. RECORD 1 STOREDUSING DRBO: [ILSMGR. ILS]WD1027.DRBO:[ILSMGR.ILS]WD1032. RECORD 2 STOREDUSING DRBO:[ILSMGR.ILS]WD1028.DRB0:(ILSMGR.ILS]WD1032. RECORD 3 STOREDUSING DRBO: [ILSMGR.ILS]WD1029.
-DRB0:[ILSMGR.ILS]WD1032. RECORD 4 STOREDUSING DRBO:[ILSMGR.ILS]WD1030.DRBO:[ILSMGR.ILS]WD1032. RECORD 5 STORED .--
$ FIL 1031DRBO:[ILSMGR.ILSJWD1031. RECORD DATA
12 DK BLKS, 5 RECORDSPRIMARY FILE
$ FIL S1033*DRBO:LILSMGR.ILS1WD1033. DOES NOT EXIST* SECONDARY FILE
$ OPN S3$ SME 6,2Do YOU WANT VARIANCE RATIOS PRINTED? (Y OR N)
.- >
*DRBO:[ILSMGR.ILS]WD1033. RECORD 4 STORED* $ FIL S1034
C-4
.
DRB0: [ILSMGR.ILS]WD1034. RECORD DATA12 DK BLKS, 0 RECORDS
SECONDARY FILE$ PCO 2,1033 .
USER$$DISK:.[ILSMGR.ILSWD1034. RECORD 5 STORED
USER$$DISK:[ILSMGR.ILS]WD1035. RECORD 5 STOREDPlot the resaults using $ PLR$ PLRILS PLOTTING ROUTINE
UP TO 20 INPUT FILESUP TO 1024 POINTS PLOTTED
ENTER X-COMPONENT->1A
ENTER Y-COMPONENT->2ENTER FILE NO., DISK NO.AND NO. CONSECUTIVE FILESDEFAULTS TO DRBO: [ILSMGR.ILS]WD1031.
->1034, ,2SYMBOLS USED ARE A-BREAD IN ANOTHER FILE? (Y,N)
->NFILES BEING READENTER SYMBOL TO PLOT, OR ENTER <ALL>
->ALLCC = CARTESIANSL = SEMI-LOGLL = LOG-LOG
- >CCAUTOMATIC SCALING? (Y,N)->YGRID? (Y,N)- >N.... -_
ENTER OPTIONE=EXITN[S,A]=NEW FILES
[START, APPEND ]C=COMPONENTSM[I]=MARK (IDENTIFY]R=REASSIGNG=GRIDS=SCALINGT=TYPE OF PLOTD=DATA TO PLOTP[N]=PLOT [NO ERASE]F[A,E,L] NI,N2=
FACTOR ANALH=HARD COPY
C-5
FILMED
3-85
DTIC
