Reduction of loudspeaker polar response aberrations through the application of psychoacoustic error concealment A.Rimell M.O. Hawksford Abstract: In a loudspeaker system it is important to have a well controlled polar response; however, with conventional multidriver enclosures off-axis phase cancellation will occur at and around the crossover frequency. To generate a uniform polar radiation pattern from any given imperfect loudspeaker cabinet, it is necessary to reduce the perceived off-axis phase cancellation due to the crossover filters. The paper proposes a correction strategy, which is then evaluated in terms of the perceived improvement. By making use of the psychoacoustic theory of masking, and developing a new strategy for time-varying filters, a creative solution was found whereby the crossover filters cause the phase cancellation to be masked from the listener, rendering it inaudible. The proposed strategy is tested using both auditory models and actual listeners as arbiters of performance. Both test methods confirm that with the proposed strategy an improvement in sound quality at an off-axis position is obtained. The on-axis sound, unaffected, remains the in- phase sum of the loudspeaker driver outputs. 1 Introduction Directionality of sound reproduction systems is an important issue for designers of high quality audio sys- tems, not only for multichannel systems and sound reinforcement systems but also for conventional two- speaker stereo reproduction systems. A major source of polar response irregularity in the midband region (where the ear is most sensitive) is cancellation at and around the crossover frequency due to the difference in the individual driver-to-listener path lengths. This work proposes a time-varying filter system with filters designed according to a psychoacoustic criterion. The off-axis errors are concealed through the utilisa- 0 IEE, 1998 IEE Pr’oceeding,r online no. 19981722 Paper first received 3rd December 1996 and in final revised form 14th October 1997 A. Rimell was with the University of Essex and is now with BT Laborato- ries, Martlesham Heath, Ipswich IP5 7RE, UK M.O. Hawksford is with the Centre for Audio Research and Engineering, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK tion of a human auditory process known as ‘frequency domain masking’. The proposed method positions the crossover frequency such that any off-axis cancellation is masked by the surrounding signal content. Such a system therefore contains time-varying filters because it uses the signal content to determine where to position the crossover frequency. The flexibility of using digital filters to perform the crossover filter function means that it is also possible to include driver equalisation in the crossover filter design. We also show that simply using very high order filters is not a sufficient solution as the perceived error is a function of programme con- tent, crossover frequency and filter order. Fig. 1 is a block diagram of the system which is described in this paper. Section 2 discusses the background theory of loudspeaker crossover filters and psychoacoustics. The main theory and implementation of the time-varying crossover filter is discussed in Section 3. Practical results obtained from listening tests and computer sim- ulation are given in Section 4. Finally, Section 5 draws some conclusions. I I model model equalisation apply crossover Fig. 1 Block diagvum of system 11
Transcript
Reduction of loudspeaker polar response aberrations through the application of psychoacoustic error concealment
A.Rimell M.O. Hawksford
Abstract: In a loudspeaker system it is important to have a well controlled polar response; however, with conventional multidriver enclosures off-axis phase cancellation will occur at and around the crossover frequency. To generate a uniform polar radiation pattern from any given imperfect loudspeaker cabinet, it is necessary to reduce the perceived off-axis phase cancellation due to the crossover filters. The paper proposes a correction strategy, which is then evaluated in terms of the perceived improvement. By making use of the psychoacoustic theory of masking, and developing a new strategy for time-varying filters, a creative solution was found whereby the crossover filters cause the phase cancellation to be masked from the listener, rendering it inaudible. The proposed strategy is tested using both auditory models and actual listeners as arbiters of performance. Both test methods confirm that with the proposed strategy an improvement in sound quality at an off-axis position is obtained. The on-axis sound, unaffected, remains the in- phase sum of the loudspeaker driver outputs.
1 Introduction
Directionality of sound reproduction systems is an important issue for designers of high quality audio sys- tems, not only for multichannel systems and sound reinforcement systems but also for conventional two- speaker stereo reproduction systems. A major source of polar response irregularity in the midband region (where the ear is most sensitive) is cancellation at and around the crossover frequency due to the difference in the individual driver-to-listener path lengths.
This work proposes a time-varying filter system with filters designed according to a psychoacoustic criterion. The off-axis errors are concealed through the utilisa-
0 IEE, 1998 IEE Pr’oceeding,r online no. 19981722 Paper first received 3rd December 1996 and in final revised form 14th October 1997 A. Rimell was with the University of Essex and is now with BT Laborato- ries, Martlesham Heath, Ipswich IP5 7RE, UK M.O. Hawksford is with the Centre for Audio Research and Engineering, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK
tion of a human auditory process known as ‘frequency domain masking’. The proposed method positions the crossover frequency such that any off-axis cancellation is masked by the surrounding signal content. Such a system therefore contains time-varying filters because it uses the signal content to determine where to position the crossover frequency. The flexibility of using digital filters to perform the crossover filter function means that it is also possible to include driver equalisation in the crossover filter design. We also show that simply using very high order filters is not a sufficient solution as the perceived error is a function of programme con- tent, crossover frequency and filter order. Fig. 1 is a block diagram of the system which is described in this paper. Section 2 discusses the background theory of loudspeaker crossover filters and psychoacoustics. The main theory and implementation of the time-varying crossover filter is discussed in Section 3. Practical results obtained from listening tests and computer sim- ulation are given in Section 4. Finally, Section 5 draws some conclusions.
I I
model model
equalisation
apply crossover
Fig. 1 Block diagvum of system
11
loudspeaker cabinet
(low frequencies)
L
Fig, 2 Active-loudspeaker system
amplifier
2 Time-varying crossover filters: Background theory
2. I Loudspeaker crossover filters To produce the wide frequency response required for the human hearing system (20Hz to 20kHz), it is neces- sary to use two or more loudspeaker drive units. This is because standard driver transducers can only produce a portion of the frequency spectrum accurately, due to their bandpass frequency domain characteristics. A typ- ical loudspeaker cabinet will contain two driver units. A ‘woofer’ recreates the lower half of the audio spec- trum and a ‘tweeter’ recreates the upper half of the spectrum. Three-way systems, employing a midrange unit, are also used; however, for the purpose of this paper only two-way systems are considered. Because each of the two drivers operates within a limited fre- quency band, it is necessary to prevent a driver being fed frequencies outside its calibrated operating region. If a tweeter were to be fed with the whole frequency spectra it would be damaged and rendered inoperable. The filter for correctly directing frequency components to individual drivers is known as the ‘loudspeaker crossover’.
Crossover filters can be implemented by using pas- sive or active filters. Passive filters consist of resistors, inductors and capacitors and are usually placed inside the loudspeaker cabinet. Active crossover filters are usually implemented with op-amps or digital filters and are contained in a separate enclosure. Implementing the crossover filters digitally (such a system is known as a ‘digital active system’) gives the designer greater flexi- bility in selecting the most suitable filter frequency response. Fig. 2 shows the connection of one channel of an active system, using two amplifier channels, low- pass and highpass, and hence a two-channel stereo sys- tem requires four amplifier channels.
2.2 Crossover filter induced error Consider the two-way loudspeaker system shown in Fig. 2, consisting of a woofer for the low frequencies and a tweeter for the high frequencies. Because the two drivers are physically separated, the only position where the listener is equidistant from both drivers is on the cabinet central axis. In Fig. 2 it is assumed that both drivers have their acoustic centre on the cabinet baffle; however, in practice the acoustic centres will be behind the baffle. At any off-axis position there will be a differential time delay introduced in the driver paths which causes a phase difference at and around the
12
crossover frequency. Fig. 3 shows the polar response of a digital 4th-order
Butterworth complementary crossover filter pair. In this plot only the crossover response is shown; the speakers are assumed to have uniform directivity and a flat magnitude response. Note that the plot has a flat on-axis frequency response and that there are dips in the off-axis response at and around the crossover fre- quency of 3kHz. The maximum value of cancellation occurs at around 24”; this is where there is the greatest phase difference between the two drivers, causing max- imum cancellation.
0 4 -5
m -10 9
- -
E -15 - 8 -20 -
30
1000
frequency
Fig. 3 Loudspeaker-crossover polar response
2.3 Psychoacoustics The coding scheme presented in this paper is based on the study of how human listeners perceive sound (psy- choacoustics). A detailed description of psychoacoustic theory is beyond the scope of this paper; however, due to its importance a brief description of frequency domain masking is given. The reader is directed towards [ 1-71 for further information on psychoacous- tics.
Frequency domain masking is the name given to the effect where a low intensity sound that can be heard in a quiet environment may cease to be audible in noisy surroundings, and the relative audibility of a particular sound might be diminished by the presence of another sound. By using psychoacoustic models [I , 71 it is possible to determine by how much one tone masks another.
IEE Proc.-Vis. Image Signal Process., Vol. 145, No. 1. February 1998
3 Error concealment using time-varying crossover filters
3.7 An overview of the proposed solution The polar response errors considered in this paper occur in a narrow band of frequencies based around the crossover frequency. Consider the example where an input signal consists of a large set of sine tones, then some of the signal spectrum will contain the polar response errors, some the desired audio signal, and some will be inaudible due to masking. If the part of the spectrum that was masked coincided with that where the off-axis errors occur, then the errors them- selves would be masked. To achieve such masking of the error it is necessary to take a short sample of the audio waveform, transform it to the frequency domain, examine the signal spectrum and design the crossover filters so that the frequency of the off-axis errors coin- cided with that of a portion of the signal which is inau- dible due to masking. The filters need to be continuously changing in sympathy with the audio waveform to be coded. The use of time-varying filters requires careful design to ensure that the changing fil- ters do not introduce a modulating noise on to the original audio signal [SI.
The crossover filter pair are generated for implemen- tation in an active digital filter system with a linear or minimum-phase response. The filters do not necessarily need to be simple Butterworth type responses (as com- monly used in active digital filter systems) and can include equalisation as necessary. The two crossover filters (lowpass and highpass) can be designed such that their on-axis responses always add up to unity, thus giving zero phase cancellation. By ensuring that the on- axis response remains unchanged only the off-axis response is modified, thus reducing the total perceived error in the loudspeaker system.
3.2 Filter selection criteria In the following subsections we discuss the process of selecting the lowpass crossover FIR filter frequency response. Three basic parameters that can be adjusted are: 1. cutoff frequency (-6dB point) 2. filter order 3. filter shape. The first two parameters assume a standard filter shape such as a Butterworth or Chebyshev, and the third parameter gives the system complete control of the fil- ter shape. Sections 3.2.1, 3.2.2 and 3.2.3 discuss each of the parameters in greater detail.
3.2. I Crossover frequency: The simplest method of crossover error concealment involves moving the crossover fvequency into a position where it is masked by the signal. The model introduced by Johnston [7] was implemented (using a 1024-point FFT and a sam- pling frequency of 44.1 kHz) to determine the masking threshold for the current frame of input signal, an example of which is shown in Fig. 4.
It is desirable to set a region within which the crosso- ver frequency may be selected, in order that the loud- speaker drivers are not subjected to audio information which is outside their rated frequency range. The range selected depends on the physical attributes of the driv- ers, and in this paper a crossover range of l .64.8kHz is taken. The frequency spectrum is divided up into
bands, the positions of which are directly related to the ‘auditory filters’ used in the human ear [9, 101. The cen- tre of each band is defined as a possible crossover fre- quency, as the position of the auditory filter frequencies is closely related to the theory of frequency domain masking [9, 21.
120 , . . . . . , , I
100
O t 4 I . . 1 1 1 1 I
2 3 4 10 10 10
frequency,Hz Power spectrum P(n), and masking threshold, T(n). for afYL2n2e Fig. 4
(1) p(4, (11) B(4, (111) CO), (lv) W ) of audco data
From Fig. 4 it can be seen that in the band from 2.8- 3.2kHz there is no audible signal (i.e. within that band all of the power spectrum is below the masking thresh- old) and hence if the crossover frequency is set at, say, 3.0kHz then the errors introduced into the signal band will be inaudible. The most suitable band is found by determining which band has the lowest value of signal- to-mask ratio. If the crossover frequency was set at 3.5kHz, which can be seen from Fig. 4 is the frequency of an audible tone, then part of the audible spectrum is distorted and the error is detected when observed from an off-axis position.
Fig. 5 shows the power output for two different crossover frequencies, calculated at 20 degrees off-axis (the worst case for the example used). The original sample sequence is the same as that shown in Fig. 4. It can be seen that there is little perceived signal degrada- tion with a crossover frequency of 3.0kHz, but when the crossover frequency is set to 3.5kHz (which could happen if , f , is fixed) it can be seen that the signal tone becomes inaudible. Thus by careful selection of the position of the crossover frequency it is possible to con- ceal the errors introduced by the off-axis cancellation.
13
The example used here has a tone-like quality (it is in fact a piano) and thus there is an obvious position in which to place the crossover. When the signal sample is noise-like (i.e. relatively spectrally flat) there may not be such a clear position for the crossover frequency, and thus a strategy for such a situation was developed. For tone-like signal frames the crossover is set to be adaptive and when the signal frame is noise-like the crossover filter remains static, removing the otherwise audible modulation of the noise-like elements. The spectral flatness measure [7] (SFM) given in eqn. 1 is used to determine how tone-like or noise-like the cur- rent signal frame is. Theoretical white noise would give an SFM of OdB, and a theoretical sine wave would give an SFM of --dB. A practical 1024-sample frame of white noise gives an SFM of =-1 dB; a sine wave of the same frame length gives an SFM of =-34dB. The non- ideal SFM value of the sine wave is due to the fact that the sine wave is windowed and then an FFT is per- formed, resulting a some spectral spreading:
(E) SFM& = lolog,,
where
I N - N
and N is the total number of frequency domain sam- ples in a frame of data.
3.2.2 Filter order: The example given in Figs. 4 and 5 uses standard 4th-order digital Butterworth filters in the crossover. It can be argued that the higher the filter order the less the overlap between the drivers and the less the off-axis cancellation. In this Section we show that the assumption that higher order filters produce less error is not necessarily valid. The perceived error is in fact a function of both crossover frequency and filter order.
Consider the ideal lowpass brick wall filter. This fil- ter’s impulse response consists of a sinc function start- ing at time = --oo and ending at time = +m. The sinc time domain response introduces ringing into the sys- tem impulse response and thus colours the system out-
1 I adaptive algorithm
put [ l l ] . Ideal brick wall filters are obviously unrealisable and therefore high-order approximations are used, and due to restrictions on filter length the width of the crossover region is finite; thus an area of frequency cancellation remains. If, in the example shown in Fig. 5, a high order filter pair with a cross- over frequency of 3500Hz were used, then cancellation of an audible tone would still occur.
Fig. 6 shows the total off-axis perceived error, as cal- culated by Johnston’s psychoacoustic masking model, for different crossover frequencies between 2 and 5 kHz with various orders of Butterworth filter pairs. The data used to generate the plot are the same as those used for Figs. 4 and 5 and are thus only valid for the frame of data shown in Fig. 4. It can be seen from Fig. 6 that an 8th-order filter at 3kHz has a lower total error than a 1024th-order filter at 3.5kHz. Assuming that a higher order filter always introduces less system error without also considering the crossover frequency is invalid.
Consequently, an adaptive crossover system could be set to find the minimum order of the filter that keeps the error within a specified range, and thus reduce time domain dispersions in the crossover filters.
required percelved output H(w)=l
A error
(generates towpass filter coefficients)
utput
Fig. 7 Block diagram of uduptive optimisution system
3.2.3 Filter shape: Sections 3.2.1 and 3.2.2 dis- cussed changing the crossover filter specification whilst using standard filter shapes (such as a Butterworth or Chebyshev); however, with digital filters it is possible to generate arbitrary filter frequency responses. The most advanced implementation of the adaptive crosso- ver system would be to make the whole system adap- tive; thus by using an optimisation algorithm it should be possible to generate recursively the lowpass filter coefficients such that the perceived error is minimised. Fig. 7 shows the block diagram of the proposed system.
Filters need to be designed to meet the error conceal- ment criteria, and thus it is necessary to develop an optimal digital filter. As the masking changes continu- ously with the signal content and as the psychoacoustic model is nonlinear many of the standard filter design techniques are inappropriate. The main constraint is that the filters must retain their lowpass and highpass characteristics, as the main function of loudspeaker crossover filters is to prevent the loudspeaker drivers being fed frequencies outside their normal operating range. This constraint limits the usefulness of tradi- tional adaptive filters, such as LMS and Kalman filters [12, 131, because whilst reducing the error they also destroy the lowpass and highpass characteristics, thus making the filters unusable.
By using a genetic algorithm (GA) [14] it may be possible to develop a filter pair which will produce a minimal amount of audible error [15, 161, whilst retain- ing the required low/highpass characteristics.
3.3 €9 ualisa tion In practice the loudspeaker drivers used will not have an ideal bandpass frequency response. By taking the drivers’ frequency responses it is possible to design a pair of crossover filters such that they include equalisa- tion, thus correcting for anomalies in the driver responses. Using digital filters the equalisation filter design consists of taking the individual driver’s fre- quency response and inverting it. Thus, where there is a dip in the driver’s response there will be a peak in the correcting filter’s frequency response, and vice versa, thus giving an overall flat passband region.
Because of its physical construction any drive unit will be bandlimited, i.e. there will be a minimum and a maximum frequency that the driver will be able to deliver without distortion. When designing an equalis- ing filter it is important to consider the working range of the driver, and not to try to boost the signal too much at the extreme ends of its operating range. The FIR equalising filter has a frequency response which is the inverse of that of the loudspeaker driver, with a slight modification to prevent out-of-band signals hav- ing excessive gain [17-191.
The design of the equalising filters is only carried out once, for a particular set of drive units, unlike the time- varying crossover filter design presented here in which the filters are designed once for each frame of input signal. In a static crossover system (i.e. one where the crossover filter design does not change according to programme content) it is usual to combine the crosso- ver filters with the equalising filters; however, if the fil- ter shapes are being designed within the time-varying loudspeaker crossover filter system (see Section 3.2.3), it is suggested that the equalisation and crossover filter- ing operations are carried out separately to simplify the
IEE Pioc -Vis Image Signcil Process Vol 145 No I , Fchvuury 1998
time-varying algorithm. Where a look-up table of crossover filter pairs is used (for example a set of 4th- order Butterworth crossover filters with different cross- over frequencies), then the equalisation could simply be incorporated into the filters themselves, although the filters would then only be valid for a particular loud- speaker cabinet.
crossover filter number
+ i o 0
-1 0
-20
%a -30
g, -40
-50
C ._
, , , L -
:;: 1 , ,
-80
20 100 1000
frequency,Hz 10000 20000
Fig.8 (i) Tweeter bandpass function (ideal respon$e); (ii) ineasuved tweeter response; (iii) woofer bandpass function (ideal response) (iv) measured woofer response
The need f o r driver equalisation
From an examination of Fig. 8 it can be seen that it is highly desirable to incorporate equalisation into the crossover filters. The eight frequency positions corre- spond to the centre frequencies of eight pairs of crosso- ver filters (for a scheme such as that described in Section 3.2.1): the frequency values are related to the auditory filter bandwidths [9] as shown in Table 1 [20]. It can be seen that the frequency response of the two drivers at 1600 and 3400Hz are somewhat different; a change in crossover frequency from one to the other will produce a tonal change due to the change in fre- quency response. It is important to keep a uniformity in the frequency response over the range of possible crossover frequencies. There will also be a slight change due to the different driver polar responses; however, as long as the lowlmidband driver is not driven at fre- quencies which make it highly directional, then the effects are negligible.
Table 1: Frequency bands used in the across program
Lower frequency Upper frequency Crossover frequency: of band, Hz of band, Hz centre of band, Hz 1480 1720 1600
1720 2000 1850
2000 2320 2150
2320 2700 2500
2700 31 50 2900
3150 3700 3400
3700 4400 4000
4400 5300 4800
3.4 Filter implementation The program, called ucross, was written in C++ using an object oriented programming style with a proprie- tary matrix library. Sound files were played on a Sili- con Graphics Indy workstation which has an AESI EBU-SPDIF 16 bit digital audio interface [21].
In sections 3.2.1, 3.2.2 and 3.2.3 three methods of crossover filter design were described. In the UCYUSS
15
program the first of the three methods was imple- mented, where the crossover frequency is varied. This is achieved by producing a look-up table of filters with crossover frequencies in the 1.6-4.8 kHz region. Filter design by use of a genetic algorithm is currently impracticable due to the time taken to generate each filter pair. Using a look-up table of filters the program takes 5 min to process a 20s stereo sound file ~ this could be further reduced by using assembly language programming on a DSP chip. The crossover filters used included equalisation filters designed specifically for the monitor loudspeakers used to audition the processed audio.
a, 4 - b ; 3.5 0 C Q 3 - C
2.5
._
._
E
start >
-
-
I c read option &
file names
of audio data
/ f i , t e r s / + / analyse audio & select crossover filters
store current frame locate next frame
Fig.9 Systemjlowchart
Fig. 9 is a block diagram showing the function of the program: a 16-bit stereo audio sample is read in and analysed, and crossover filters are selected according to the program content and then applied to the input audio. The lowlhighpass data are then saved to disk for playback.
As the filters are continuously changing (switching between sets stored in a look-up table) it is necessary to interpolate smoothly between the sets of filter coeffi- cients to avoid any processing noise [8]. The use of a perceptually smooth filter interpolation scheme is nec- essary in a wide range of audio equipment - for exam- ple, the equalisation control on a digital mixing desk. This application is different from a digital mixing desk in that the filters need to change very quickly from one setting to another. With equipment that requires human interaction the speed of change is a function of the speed of the user (a user may take a second to change the equalisation filter), whereas the system pro- posed here may change within a data frame of approx- imately 20ms, thus increasing the likelihood of introducing processing noise.
Consider the case, for example, where the system alternately switches between two crossover filter pairs. If the filters were instantly switched in and out rather
16
than smoothly interpolated, then we can describe the output signal as a Fourier series representing the time- domain waveform modulated by a square wave (amplitude modulation). It can be shown, by calculation of the Fourier series, that square-wave modulation produces harmonics that decay with lln, where n is the harmonic index. If a linear interpolation were employed to change between filters a triangular- wave modulation would occur, resulting in harmonics which decay at a rate of lln2. It therefore follows from Fourier series analysis that a sinusiodal interpolation scheme would produce only two harmonics (sum and difference) which are spectrally close to the fundamental frequency.
Pieces of audio were filtered with a pair of time-vary- ing filters using step, linear and sinusoidal interpolation schemes. The resultant signals were played to a panel of listeners (without them knowing which signal was which) and they all noticed modulation tones with the step and linear interpolation. No modulating tones were noticed with the pieces of audio processed with a sinusiodal interpolation scheme; this result was con- firmed by passing all of the audio pieces through a psy- choacoustic masking model [7]. The model showed that the two harmonics generated with a sinusoidal interpo- lation scheme were inaudible due to masking effects, whereas with the other interpolation schemes the mask- ing model showed that the harmonic components would indeed by audible.
The system used a frequency domain interpolation scheme, where the filter frequency responses changed smoothly in the frequency domain, thus ensuring that each intermediate filter had a similarly shaped frequency-magnitude response to that of the original crossover filter. As described above, a sinusoidal interpolation envelope was used to interpolate between filters.
4 Results
To test the adaptive crossover algorithm, a selection of speech and musical samples, with a wide variety of styles, were recorded on to a hard disk and then coded with both a fixed and an adaptive crossover algorithm. Two methods of evaluation were used: an off-axis model combined with a psychoacoustic model [ 11 and listening tests with a group of test subjects.
1.5 2 l 1 1 ,
150 200 250 300 350 400
time (swept frequency)
Fig. 10 __ adaptive; ~ ~ ~ fixed Scores: 1 Very annoying; 2 annoying; 3 slightly annoying; 4 perceptible, hut not annoying; 5 imperceptible
Output of perceptual model with MOS scale: Swept sine wave
IEE ProcVis. Image Signal Process., Vol. 145, No. 1, February 1998
The first test sample consisted of a swept sine wave. As the swept sine wave passes through the crossover region, off-axis cancellation occurs, causing a null at and around the crossover region. Fig. 10 shows the perceived off-axis sound (a comparison of the original on-axis signal with the coded off-axis signal) as determined by a psychoacoustic model. It can be seen that with a fixed (conventional) filter the null around the crossover frequency is clearly audible whereas with the adaptive filter there is little perceived degradation to the signal. The output of the psychoacoustic model was also confirmed by listening to an actual active- crossover loudspeaker system at on-axis and off-axis positions.
Listening tests were carried out with the active-cross- over loudspeaker system, examining the other coded samples by comparing the on-axis and off-axis responses. The improvement in sound quality was greatest for tonal signals such as solo classical instru- ments. For the worst case example (white noise) the fixed and adaptive coding could not be distinguished - in other words for the worst case scenario the sound does not change but in other cases the sound is improved. Owing to the complementary nature of the high- and lowpass crossover filters the on-axis response is always the in-phase sum, correctly recreating the original sound. The tests were carried out in a simu- lated living room containing carpets, soft chairs and curtains, which was necessary to reduce room effects to a typical level. For a detailed description of the effects a room can have on an audio signal (see [22, 21).
Table 2: Listening test results of 14 subjects
Adaptive Fixed better better than than adaptive, fixed, % %
Listener Don‘t Trained number know, % listener?
1
2
3
4
5
6
7
8
9
10
11
12
13
14
100
95
100
100
100
100
50
60 100
100
100
50
70
95
0
0
0
0 0
0
0
0 0 0
0
0 0
0
0
5
0
0
0
0
50
40
0
0
0
50
30
5
Y
Y
Y Y Y
Y
N N
N
N
N N
N
N
20 random double-blind presentations of a piece of classical guitar music with ten having fixed filters and ten having adaptive filters. For each piece the listener was free to move around the loudspeaker to compare on- and off-axis responses
As an example we shall consider the results of listen- ing tests performed on a piece of classical guitar music coded with fixed and adaptive filters, and listened to at an on- and off-axis position. Table 2 contains the results from the listening tests. Test subjects consisted of a mixture of trained and untrained listeners (a trained listener is one who is experienced in carrying out listening tests and is familiar with the sound of
IEE Proc.-Vis. Image Signal Process., Vol. 145, No. 1, February 1998
errors in audio systems; an untrained listener is a mem- ber of the general public). The results show that almost all of the test subjects perceived the adaptive crossover encoded sample as being more like the original sample than that with the fixed crossover. Two of the 14 test subjects could not distinguish between the two samples and none preferred the fixed filter to the adaptive one. All subjects agreed that there was no audible process- ing noise caused by the filter coefficients changing with every frame of audio signal.
5 Conclusions
In this paper a method of dealing with errors in two- way loudspeaker systems has been proposed. The methodology employed is based on the principle of error concealment utilising psychoacoustic criteria and is summarised by Fig. 1.
Any multidriver loudspeaker system will have a non- uniform polar frequency response due to the physical separation of the drive units. The amount of nonuni- formity is related to the crossover filter order, but high order crossovers will still exhibit off-axis cancellation. Whilst it is not possible to generate a flat polar fre- quency response with a multidriver system, it is possi- ble to position the error such that it is not detectable by a human listener. To achieve this it is necessary to base the algorithm on an understanding of the human auditory perception system.
It was found that for simple sine wave based test sequences the adaptive system produced a significant improvement in sound quality (i.e. the off-axis errors were successfully masked by the surrounding material). For a wide range of typical audio excerpts an improve- ment was obtained which a panel of trained and untrained listeners noticed. The system tested com- prised a look-up table of 4th-order Butterworth crosso- ver filters. Using a genetic algorithm may produce an even greater perceived improvement but is not practica- ble at present due to the immense amount of comput- ing power required.
6
1
2
3
4
5
6
I
8
9
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