1 In troduc t ion As IN THE human heart, there is electric activity in the stomach. This electrogastric activity can be measured both intraluminally and cutaneously and the signals measured are very useful for medical research and in clinical diag- nosis. The cutaneous gastric measurement, often called electrogastrography (EGG), is especially attractive because it is noninvasive, completely harmless to patients or volun- teers and does not disturb the on-going gastric activities.

Since Alvarez's first announcement of cutaneous gastric measurements in 1922 (ALVAREZ, 1922), a great deal of research efforts have been expended on investigating the relationship between recorded gastric signals and specific activities of the stomach in question. Unlike other electro- physiological measurements such as electrocardiography (ECG) and electroencephalography (EEG), however, the progress of the applicability of the methods has been very slow. One of the most important reasons for that is the poor quality of the measured signals, i.e. the weakness of the real gastric signal and the heavy disturbances which arise from the heart and the diaphragm. Signal-processing techniques which have been applied to improve the quality of gastric measurements include bandpass filtering (GOODMAN et al., 1955; NELSEN and KOHATSU, 1968; STOD- DARD et al., 1981), fast Fourier transformation (BROWN et al,, 1975; and VAN DER SCHEE and GRASHUIS, 1983, 1987), phase-lock filtering (SMALLWOOD, 1978), autoregressive modelling (LINKENS and DATARDmA, 1978) and adaptive filtering (KENTXE et al., 1981a, b; CHEN et al., 1987a, b). However, research into improvements of the recording and

First received 16th February and in final form 2nd August 1988 �9 IFMBE: 1989

processing techniques is still one of the main areas of endeavour, as Abell and his colleagues said: 'We must await future improvements in EGG recording techniques and waveform analysis' (STERN and KOCH, 1985, p. 87).

Both intraluminally and cutaneously measured gastric signals consist of a real gastric signal component, ECG, respiratory artefact, motion artefacts and noise resulting from the electrode/skin interface. Among these the ECG and the respiratory artefact are the main disturbances.

The normal frequency of the gastric signal component is around 0.5 Hz (or 3 cycles min-1), and those of the ECG and respiratory artefact are about I Hz and 0.2-0.4Hz, respectively. Elimination of the ECG is not difficult and can be performed by conventional low-pass filtering because its frequency is much higher than that of the gastric signal component. The respiratory disturbance is, however, a common and thorny problem. It is superim- posed upon almost all the gastric measurements. In some recordings it may completely obscure the real gastric signals. Moreover, the frequency of the real gastric signal can approach that of the respiratory artefact during some abnormal activities of the stomach, particularly during the appearance of tachygastria. This renders conventional frequency-domain filtering techniques useless.

From the above discussion we observe that 'the impor- tance of ruling out respiratory artefact, especially upon the external EGG but also on the internal EGG and mano- metric tracing, cannot be overstressed' (STERN and KOCH, 1985, p. 85). It is the aim of this paper to show that adapt- ive filtering (WIDROW et al. 1975) is an effective and practi- cal method for cancellation of the respiratory artefact in both intraluminal and cutaneous gastric measurements.

Medical & Biological Engineering & Computing January 1989 57

2 Descript ion of the measurement Volunteers for the measurements were healthy adults

and had fasted for more than 15 h before the experiments. They were asked to lie on their back and to keep as still as possible. For the cutaneous measurements seven Ag/AgCl electrodes (red dot, 3M) were positioned at different spots on the abdominal skin outside the stomach as shown in Fig. 1, where the distance between two adjacent electrodes

Fig. 1

/

Positions of electrodes on the abdomen

was equal to 3cm. One of the electrodes was used as a common reference and six bipolar signals were derived by connecting the reference electrode with each of the others. The intraluminal bipolar gastric signal was measured by swallowing a small tube with two suction electrodes in it. The distance between these two electrodes was 3 mm. Pre- amplifiers with a time constant of 5s (corresponding to 0.03Hz) were used for both intraluminai and cutaneous signals. A reference respiratory signal was measured by positioning a small balloon on the abdomen near the diaphram. The small balloon was filled with water and connected with a pressure sensor. All of these eight signals were amplified by a Universal Amplifier 854 with a cutoff frequency of 5 Hz for the cutaneous signals and 30 Hz for the intraluminal signals. They were recorded simulta- neously on an analogue tape and on Mingograf paper. A higher cutoff frequency (30Hz) was used for the intralu- minal signal to monitor spike activities in the stomach on the recording sheets. The stored analogue signals were first digitised through an 8-channel 12-bit A/D convertor and sampled at a frequency of 12 Hz for the cutaneous signals and 96 Hz for the intraluminal signals. These digital signals were then low-pass filtered using a digital finite impulse response (FIR) filter with a cutoff frequency of 1 Hz and sampled again at the frequency of 2Hz. The waveform analysis and signal processing were performed in a Vax computer.

Typical measurements are shown in Fig. 2. Fig. 2a is the

C

Fig. 2 Measurements of electrogastric signals and respiratory signal: (a) bipolar cutaneous signal; (b) bipolar intralu- minal signal; ( c ) reference respiratory signal

bipolar cutaneous signal, Fig. 2b is the intraluminal signal and Fig. 2c is the reference respiratory signal. The slow waves in Figs. 2a and 2b are the gastric signal component, and the superimposed spike-like components are the ECG. The respiratory artefact, which is very heavy in the cut- aneous signal, can be easily observed when compared to Fig. 2c. Figs. 3a and Fig. 3b show the power spectra of

58

-110

m -130 "o

-150 o o.

-170

-190 0

- 130

i i I I I

0 2 0.4 0.6 0 8 1.0 f r equency , Hz

- 150

"~. -170

o -190

-210

-230 ' ' ' ~ J

0 0.2 0 4 0 6 0 8 10

f requency . Hz

b

Fig. 3 Power spectra of (a) cutaneous gastric signal and (b) respiratory signal

Figs. 2a and Fig. 2b, respectively. The first peak from the left in Fig. 3a is the gastric signal component at a fre- quency of about 0.05Hz. The peak in Figs. 3a and 3b around 0-3 Hz is the contribution of the respiratory arte- fact. To prove the origins of the different frequency com- ponents in the cutaneous signal, the power spectra of the correlation functions between the cutaneous and intralu- minai signals and between the cutaneous signal and the reference respiratory signal are calculated and shown in Figs. 4 and 5, respectively (RAmNER et al. 1979). Fig. 4 is

50

40

30 I io

0 I I I I I I I I I I

0 0.2 0,4 0.6 0 8 1,0 f r equency . Hz

Fig. 4 Cross power spectrum between the cutaneous and the intraluminal gastric signals

the power spectrum of the correlation function between the cutaneous and the intraluminal signals. The peak at 0.05 Hz proves that the slow wave in the cutaneous signal is really from the stomach. The power spectrum of the correlation function between the cutaneous and respir- atory signals is shown in Fig. 5. It has a higher value

Medical & Biological Engineering & Computing January 1989

5

-5 m

. t_

~o '~ -15

- 2 5 i t i i t i i i i J 0 0"2 0 "4 0 ' 6 0 "8 I "0

f r e q u e n c y , H z

Fig. 5 Cross power spectrum between the cutaneous gastric signal and the reference respiratory signal

around 0.3 Hz, which shows that the frequency component around 0.3 Hz is respiratory artefact.

As shown in Fig. 3, the normal frequency of the gastric signal component is about 0.05 Hz and that of respiration is around 0.3Hz. They are far apart, which gives the impression that the conventional low-pass or bandpass filter can be applied to eliminate the respiratory artefact. Unfortunately, however, the frequency of the gastric signal can in some cases be higher and may approach that of respiration as indicated by STERN and KOCH (1985). This implies that conventional filtering techniques cannot be applied in the frequency domain. To solve the problem an adaptive filtering technique in the time domain is proposed in the following section. It should be stressed that this technique is simple and very efficient. Experiments show that by applying the proposed method the respiratory artefact can be eliminated, while the real gastric signal is not affected.

3 Adaptive cancellation of the respiratory artefact

3.1 Principles of adaptive noise cancellation In this section we present a brief overview of the struc-

ture and the derivation of an adaptive noise canceller (Fig.

d j = S I §

p r i m a r y i n p u t

xj = n l j

r e f e r e n c e i n p u t

wl i

Xj -n+1

_- , 4- . [

I

b Fig. 6 Adaptive noise canceller: (a) block diagram; (b) tapped

delay line

Medical & Biological Engineering & Computing

6). More details can be found in WIDROW et al. (1975). The adaptive filter (AF in Fig. 6a) consists of a so-called tapped delay line. The detail of the adaptive filter is shown in Fig. 6b. The inputs xj, xj-x . . . . . xj_,+ 1 are weighted by n adjustable filter coefficients w u , w2j . . . . . w,j according to the least mean-square (LMS) algorithm to produce the output yj. In the figure z -~ stands for one sample delay and j stands for the time instant.

Let us define

x j = [xj, x j_ , , . . . , x j _ , + d T (1)

as the input vector and

Wj = [w,j , w2j . . . . . w . J (2)

as the filter weight vector. The output yj is equal to the inner product of Xj and Wj

yj = X'fWj = 14ffj Xj (3)

The weights of the adaptive filter are adjusted for every input sample with the aim of minimizing the mean-square error. Assuming that the filter input signal xj and the primary input dj (Fig. 6a) are statistically stationary, a general expression for the mean-square error as a function of the weight vector can be derived as follows:

ej = dj - yj = dj - X r Wj (4)

E l 4 ] = E[df] - 2 p r w j + 14ffjRWj (5)

Where E [ ] stands for the expectation, P is the cross- correlation vector defined by

P = EEdjXj] (6)

and R is the input correlation matrix defined by

R = EEXjXf] (7)

Using the steepest-descent method and approximating gra- dient mean-square error by gradient square error

wj+, = wj - ~vj (8)

Vj = ae~/awj (9)

The Widrow-Hoff LMS algorithm (WIDROW et al., 1975) is derived:

Wj +, = Wj + 21~ej Xj (10)

where p is the step-size which controls the stability and the rate of the convergence. The larger the value of #, the faster the algorithm converges and the more the gradient noise is introduced, and vice versa.

The LMS algorithm requires that the next weight vector Wj+~ is equal to the present weight vector Wj plus a change proportional to an estimate of the negative gra- dient of the error surface. After the convergence of the algorithm the weight vector obtains its optimal value and the mean-square error is minimised.

Examination of Fig. 6 reveals how the noise in the primary input can be cancelled if the LMS algorithm has converged. Consider that in Fig. 6a the primary input d consists of a signal s and noise no (for convenience the subscript j standing for the time instant is omitted). The reference input, i.e. the input of the adaptive filter, consists of noise n 1. s o is assumed to be uncorrelated with both n o and n~. n o and nx are assumed to be correlated with each other in some unknown way. The noise n~ is adaptively filtered to produce an output y which is then subtracted from the primary input to produce the system output e.

e = s + n o - y (11)

e 2 = s z + (no -- y)2 + 2s(no - y) (12)

January 1989 59

Taking the expectation of both sides of the above equation and observing that s is uncorrelated with no and with nl, we have

E[e 2] = E[s 2] + E[(n ~ _ y)2] + 2E[s(no - y)]

= E[s 2] + E[-(n0 - y)2] (13)

From the above equation we observe that the mini- misation of the mean-square error can only result from the minimisation of El(n0 - y)2], i.e.

min E[e 2] = E[s 2"] + min El(no - - y)2] (14)

It can be seen from this equation that the smallest possible output power is E[e 2] = E[sZ]. When this is obtained El(no - y)2] = 0; therefore, the output y of the adaptive filter is a replica of the noise no in the primary input and the noise no is eliminated in the system output, i.e. e -- s.

Generally, we conclude that, after the convergence of the LMS algorithm, the output of the adaptive filter yj is, in the sense of the mean-square error, equal to that part of the primary input which is correlated with the input of the adaptive filter.

3.2 Cancellation of the respiratory artefact Having introduced the principles of the adaptive noise

cancellation and the LMS algorithm, we present the prac- tical adaptive system for the elimination of the respiratory artefact in the electrogastric measurements. The proposed system is shown in Fig. 7, where A stands for a bulk delay,

signal ~

Fig. 7

si+r i " ~ ~ - - e J

primory input system output

respiratory signal Adaptive system for cancellation of respiratory artefact

AF for the LMS adaptive filter, sj for the real gastric signal, rj for the respiratory artefact and nj for some other noise. The system contains two stages. The primary input of the first stage is a low-pass filtered (cutoff frequency 1 Hz) measurement which consists of a real gastric signal, respiratory disturbance and some other nonperiodic noise. The input to the first adaptive filter is simply a delayed version of the primary input. /X is chosen to be long enough to decorrelate the noise n~ so that the output of the adaptive filter is just a replica of sj + rj because they are periodic and cannot be decorrelated. Consequently, this stage performs the function of preprocessing.

The primary input of the last stage is the output of the first adaptive filter which consists of real gastric signal and respiratory artefact only. Its reference input ?j is the simul- taneously measured respiration signal which is correlated with rj in the primary input as shown in Fig. 5. According to the conclusion of the previous section, the system output e~ is free of respiratory artefact because the output of the last adaptive filter is a replica of the respiratory artefact rj and it is subtracted from the primary input of the last stage.

4 Per formance analysis Based on the LMS algorithm, an adaptive system has

been proposed in the previous sections for the cancellation of the respiratory artefact and the white noise. The LMS

6 0

algorithm is derived according to the stochastic gradient method. For convenience, it is repeated here:

Wj+ 1 = Wj q- 21tejXj (15)

where ej is the residual error between the primary input and the output of the adaptive filter, and Xj is the input signal vector to the adaptive filter.

Starting with any initial values (usually zeros), the weight vector is adaptively adjusted by the LMS algo- rithm. After a sufficient number of adaptations, the weight vector attains its optimal value and the adaptive filter con- verges. From the LMS algorithm it can be seen that the convergence speed and the performance of the adaptive filter is related to the step size #. Large # means that a big step is used in searching for the optimal weights, resulting in fast convergence but on the other hand generating more gradient noise in the steady state. If the signals dj and x i are stationary in the steady-state, the next weight vector Wj+I should be equal to the current one, Wj. Thus, the second term on the right hand side of eqn. 15 is a noise term. Consequently noise is introduced at the output yj of the adaptive filter, or, in other words, the filter is mis- adjusted.

To investigate the performance of the adaptive filtering system shown in Fig. 7. We define a quantitative term 'misadjustment (M j)' as follows:

Mj -= E [ ( s j - ej) z] (16)

where sj is the gastric signal component in the measure- ment and ej is the noise-free output of the adaptive system. The misadjustment reflects the degree of the waveform dis- tortion of the interested signal component introduced by the adaptive system.

From eqn. 15 and Fig. 7 it can be seen that Mj is related to the value of/~ and the signal-to-noise ratio (SNR) of the measurement. The higher the value of/~ and the level of noise n are, the larger the misadjustment will be.

Because the real gastric signal component in the mea- surement is unknown, the misadjustment cannot be calcu- lated. Thus, several computer simulations were conducted using the following test signals:

(a) gastric signal sj: s i = A~ sin (2nf~j) (b) respiratory artefact rj: rj = A, sin (2nf, j) (c) white noise nj: nj = A,(~j - 0"5). ~j is uniformly distrib-

uted (0, 1) random noise (d) the input to the system is a combination of the above

three signals: dj = sj + r j + nj (e) reference signal ?j: Pj = 0"934rj§ t5 is an integer with

random value.

4.1 Cancellation of the respiratory artefact Fig. 8 shows a simulation result with the following

parameters:

f~ = 0.25 H z f , -- 0.3Hz A~ = A, = IA, = 0

5 s I I Fig. 8 Simulation without white noise. (a) Simulated #astric signal

component sj; (b) simulated system input d~; (c) system output

Medical & Biological Engineering & Computing January 1989

Because white noise is assumed to be absent, the first stage of the system (Fig. 7) is skipped. Fig. 8a shows the simu- lated gastric signal sj; Fig. 8b shows the simulated input signal dj applied to the system and Fig. 8c is the output of the system ej. Comparing curves a and b one can be con- vinced that the system performs well in cancelling the res- piratory artefact.

4.2 Convergence of the system The convergence of the system is illustrated in Fig. 9,

0"25

0.20

E 0.15 .~_ ~ 0.10 E

0.05

0 I 1 I I I I I I I J

0 200 400 600 800 1000 adaptation number

Fig. 9 Convergence of the adaptive system (misadjustment against adaptation number.)

where the vertical axis is the misadjustment Mj over 200 individual runs and the horizontal axis the adaptation number. The conditions for the experiment were the same as the previous one except that A, = 0.5 (white noise was also included) and the whole system was utilised. It can be seen that, as the number of the adaptations increases, the misadjustment becomes smaller. After 1000 adaptations the misadjustment is equal to about 0.018. The system converges after 2000 adaptations and the misadjustment equals 0.013 in the steady state.

4.3 Influence of different noise levels The result shown in Fig. 8 was obtained from the experi-

ment in which the white noise was assumed to be absent. In real gastric measurement, besides the respiratory arte- fact some other noise is present, which is assumed to be white. We have stated before that the performance of the adaptive system is related to the SNR level. One experi- mental result showing the effect of a high noise level is presented in Fig. 10 for the following parameters, setting:

fs = 0"25 H z f , = 0'3 Hz As = 0-5A, --- I '0A, = 1"0

a ~

5s

Fig. 10 Simulation with unusually low SNR. (a) Simulated gastric signal component sj; (b) system input dj; (c) the preprocessing output; (d) system output e~

Table 2 Optimisation of the step size

Fig. 10a shows the simulated gastric signal component contained in the system input signal shown in Fig. 10b. Fig. 10c is the output of the adaptive filter at the first stage, from which the cancellation of white noise is clearly seen. The final output of the system is shown in Fig. 10d. The waveform distortion of the gastric signal component when the SNR is low (in this case the SNR is less than 0 dB) can be observed from that curve.

The influence of different noise levels is shown in Table 1, where the first row shows different levels of the white

Table 1 Influence of the noise level

A, 0.1 0'3 0.5 1.0 2.0 4.0

M 0.0056 0"0083 0.0135 0-0340 0.0836 0'1699

noise (the other parameters are fixed as in Fig. 10) and the second row shows the misadjustments M in the steady state. It can be seen that as the noise level rises, the mis- adjustment becomes larger.

4.40ptimisation of the step size The step size is an important factor in controlling the

convergence speed and the performance of the LMS adaptive filter. In a stationary environment a smaller value of # results in a better performance (smaller M). In a non- stationary environment, however, this is not always true. Smaller values of # make the adaptive filter less capable of following the statistical changes of the input signals and more difficult to reach the optimal state (CHEN and VAN- DEWALLE, 1988), thereby resulting in larger misadjustment. Thus the optimal value of/a is a compromise between less gradient noise (small/~) and a fast convergence (large/t).

The optimisation of the step size is shown in Table 2, where the first row presents different values of/~1,/-~2 ( f o r

the first and second adaptive filters, respectively) and the second row, the corresponding misadjustments in the steady state. #1 and/-~2 are related to the step size p in the following way:

l /~ - ( 1 7 )

/~x(#2) x P

where P is the total input power to the adaptive filter. The other parameters are chosen as follows:

fs = 0"25 Hzf r = 0-3 Hz A s = 0"5A, = I '0A, = 1'0

It can be seen in Table 2 that the optimal value of/~t(/~z) is 100. Other values larger or smaller than that result in larger misadjustments.

For all other simulations described in this section the optimal value of/a is used.

4.5 Nonstationary effects of the respiratory artefact To see the effect of the time variations of the respiratory

artefact on the performance of the system, a nonstationary respiratory signal is simulated as a sequence of sinus signals

r j = A, sin (2~J~j) (18)

each considered over one full period. The amplitude ,zT, and the duration 1/~ of each sinusoid vary as

,4, = A,(Damt,(~z - 0"5) + 1"0) (19)

= f v ( D f r e q ( f i - - 0"5) q- 1"0) (20)

~1, P2 10 25 50 75 100 200 300

M 0.0803 0.0322 0.0223 0 -0211 0 . 0 2 0 9 0.0232 0.0269

Medical & Biological Engineering & Computing January 1989 61

Table 3 Nonstationary effects

D~ y, e q = 0), D y,,q(D=m p = 0), per cent M per cent M

ne t x~ - 5

~t o - i s

0 0.0135 0 0.0135 10 0.0137 10 0.0368 20 0.0155 20 0.0245 40 0.0239 40 0-1637 80 0.0567 80 0.0546

The effects of the different values of the amplitude D=,,p and the frequency Di,eq deviations are listed in Table 3. From the first two columns we can see that larger devi- ations of the amplitude increase the misadjustment. The deviation of the frequency also affects the performance of the system (see last two columns). From columns 3 and 4 no clear relationship between the value of Ds,e~ and M can be derived. However, it seems that the deviation of the frequency has a larger influence on the performance than does the amplitude.

It has also been proved that, as the frequencies of the gastric signal component and the respiratory artefact get closer, the performance of the system becomes better. Under the same condition, M is 0.02093 for f~ = 0.25 Hz, f, = 0.3 Hz, whereas M = 0.0103 for fs = 0.29 Hz, f, = 0.3 Hz.

It should be noted that in all simulations we have assumed that the respiratory artefact has a higher (or equal) level than that of the real gastric signal component. According to the analysis of real gastric measurements, the levels of respiratory artefact and the other noise are usually lower than that of the gastric signal component, i.e. worse conditions have been simulated.

Based on the computer simulations we conclude that the adaptive system exhibits a good performance for a station- ary input signal with a reasonably low SNR. In the case of nonstationary input or very low SNR, the respiratory artefacts can still be effectively cancelled while the gastric signal component is only slightly distorted.

5 Results Experiments with both intraluminal and cutaneous mea-

surements have been carried out by applying the system shown in Fig. 7. The results are shown in Figs. 12-14.

The parameters in Fig. 7 for those experiments are chosen as follows: the length of the tapped delay line of the adaptive filters should be long enough to cover at least the whole period of the frequency component of interest (WIDROW et al. 1975). The first adaptive filter should produce a replica of s + r and the periods of s and r are about 40 and 8 samples, respectively (since the sampling frequency is 2 Hz). Therefore, it is chosen to be 50 samples. The second adaptive filter produces only the replica of R, so that the length of its tapped delay line is chosen to be 10 samples. The delay A is chosen to be 1, though its value is not very sensitive according to our experience. The step size/~ is set to be 0.01 P for the first stage and 0.05 P for the last stage, where P is the estimated input energy to the adaptive filter.

62

- 2 5

- 3 5 i I I I I I 1 I

0 0-1 0-2 0.3 0 4

f r e q u e n c y , Hz

Power spectra of the input cutaneous gastric signal (upper line) and the respiratory artefact cancelled output (lower line)

20

Fig. 12

0 n n "10

Ib

O

~" - 20

Fig. 13

where ~ is a uniformly distributed (0, 1) random noise. The simulated respiration is a sinusoidal-like signal with

random changing frequency and amplitude as shown in Fig. 11.

5s I 4

Fig. 11 Simulated nonstationary respiratory signal

- 4 0 t i J J J i i J

0 0 1 0"2 0 ' 3 0 4

f r e q u e n c y , H z

Power spectra of the input intraluminal gastric signal (upper line) and the respiratory artefact cancelled output (lower line)

t_. 100S ._a

F i g . 14 The result of Fig. 9 shown in the time domain. (a) Input signal; (b) output signal

The processed result of a cutaneous measurement is shown in Fig. 12. The upper line is the power spectrum in dB of the measurement and the other line is that of the processed result. Fig. 13 shows the result for our intralu- minal measurement. The upper line is the power spectrum of the measurement and the other is the processed result. We can observe from these two figures that the respiratory components (around 0.3 Hz in Fig. 12 and 0.38 Hz in Fig. 13) are almost completely eliminated. The gastric signal component, however, is not affected. The result of Fig. 13 in the time domain is shown in Fig. 14, where a is the original measurement and b is the processed output. The cancellation of the respiratory artefact can be observed visually in this figure.

6 Conclusion Both intraluminai and cutaneous signals as well as refer-

ence respiratory signal are measured. The cross- correlations between the cutaneous and intraluminal signals and between the cutaneous and the respiratory

Medical & Biological Engineering & Computing January 1989

signal have been calculated so that the origins of the main components of the cutaneous measurement are known.

An adapt ive system for cancellation of the respiratory artefact is developed in this paper and has proved to be very efficient, i.e. the respiratory artefact is almost com- pletely removed, while the real gastric signal is not (or only slightly) affected.

Besides the cancellation of the respiratory artefact, some other noise is also cancelled by the first stage of the pro- posed system. Mot ion artefacts may also be cancelled by the last stage as the reference respiratory signal r I may also contain mot ion artefacts which are correlated with those in the gastric measurements.

The L M S algori thm is used in the adaptive filters. It is adaptive and very simple. Therefore this technique can be easily applied for online processing, such as by using a personal compute r or microprocessor.

The proposed system is also applicable in other bio- signal analysis. One of the other attractive applications is the cancellation of the respiratory artefact in intestinal measurements, where the frequencies of the interested signal and respiratory artefact overlap. Another possible applicat ion may be the cancellation of the baseline drift in electrocardiographical signals.

related, low-frequency components in canine electro- gastrographic signals. Am. J. Physiol. 245, G470-G475.

VAN DER SCHEE, E. J. and GRASHUIS, J. T. (1987) Running spec- trum analysis as an aid in the representation and interpretation of electrograstrographic signals. Med. & Biol. Eng. & Comput., 25, 57-62.

WIDROW, B., GLOVER, J. R. Jr. McCOOL, J. M., KAUNITZ, J., WILLIAMS, C. S., HEARN, R. H., ZEIDLER, J. R., DONG, E. J. Jr., and GOODLIN, R. C. (1975) Adaptive noise cancellation: prin- ciples and applications. Proc. IEEE, 63, 1692-1716.

Authors' biographies Jiande Chen was born in Zhejiang, China on the 4th December 1956. He received a BS from East China Normal University, Shanghai, China in 1982. Since December 1983 he has been studying at the Katholieke Universiteit Leuven, Belgium, where he is currently final- ising his doctoral research in electronic engin- eering. His research interests are mainly on the adaptive signal processing and its applications

in biomedical engineering and telecommunications.

References ALVAREZ, W. C. (1922) The electrogastrogram and what it shows.

J. Am. Med. Assoc., 78, 1116-1118. BROWN, B. H., SMALLWOOD, R. H., DUTmE, H. L. and SXODOARD,

C. J. (1975) Intestinal smooth muscle electrical potentials recorded from surface electrodes. Med. & Biol. Eng., 13, 97-103.

CHEN, J., VANDEWALLE, J., SANSEN, W., VANTRAPPEN, G. and JANSSENS, J. (1987a) Adaptive enhancement of human electro- gastrography. Proc. 9th Ann. Conf. of IEEE/Eng. in Med. & Biol. Soc., Boston, USA, Nov. 1987, 858-859.

CHEN, J., VANDERWALLE, J., SANSEN, W., VANTRAPPEN, G. and JANSSENS, J. (1987b) Adaptive cancellation of respiratory dis- turbance in electrogastric signals. Proc. Int. Conf. on Digital Signal Processing, Florence, Italy, Sept. 1987, 901-905.

CHEN, J. and VANDEWALLE, J. (1988) An /~-vector LMS adaptive system for enhancing nonstationary narrow band signals. Proc. IEEE Int. Symp. on Circuit and System, Finland, June 1988, 771-774.

GOODMAN, E. N., COLCHER, H., KATZ, G. M. and DANGLER, C. L. (1955) The clinical significance of the electrogastrogram. Gas- troenterol. 29, 598-607.

KENTIE, M. A., VAN DER SCHEE, E. J. GRASHUIS, J. L. and SMOUT, A. J. P. M. (1981a) Adaptive filtering of canine electro- gastrographic signals. Part l : System design. Med. & Biol. Eng. & Comput., 19, 759-764.

KENTIE, M. A., VAN DER SCHEE, E. J., GRASHUIS, J. L. and SMOUT, A. J. P. M. (1981b) Adaptive filtering of canine electro- gastrographic signals. Part 2: Filter performance. Ibid., 19, 765-769.

LINKENS, D. A. and DATARDINA, S. P. (1978) Estimation of fre- quencies of gastrointestinal electrical rhythms using autore- gressive modelling. Ibid., 16, 262-268.

NELSEN, T. S. and KOHATSU, S. (1968) Clinical electro- gastrography and its relationship to gastric surgery. Am. J. Sur#. 116, 215-222.

RABINER, L. R., SCHARFER, R. W. and DLUGOS, D. (1979) Correla- tion method for power spectrum estimation. In Programs for digital signal processing. IEEE Press.

SMALLWOOD, R. H. (1978) Analysis of gastric electrical signals from surface electrodes using phaselock techniques. Med. & Biol. Eng. & Comput., 16, 507-518.

STERN, R. M. and KOCH, K. L. (Eds.) (1985) Electrogastrography. Praeger, New York.

STODDARD, C. J., SMALLWOOD, R. H. and DUTHIE, H. L. (1981) Electrical arrythmias in the human stomach. Gut, 22, 705-712.

VAN DER SCHEE, E. T. and GRASHUlS, J. L. (1983) Contraction-

Med ica l & Biological Engineering & Computing January 1989

Joos Vandewalle was born in Kortrijk, Belgium, on the 31st August 1948. He received a degree in Engineering and a doctorate in Applied Sciences, both from the Katholieke Universiteit Leuven, Belgium in 1971 and 1976, respectively. From 1976 to 1978 he was Research Associate and from July 1978 to July 1979 he was Visiting Assistant Professor, both at the University of California, Berkeley. Since

July 1979 he has been back at the ESAT laboratory of the Katholieke Universiteit Leuven, where he is currently Professor. His research interests are mainly mathematical system theory and its applications in circuit theory, control, signal processing and cryptography.

Willy M. C. Sansen was born in Poperinge, Belgium, on the 16th May 1943. He received the engineering degree in Electronics from the Katholieke Universiteit Leuven, Belgium, in 1967 and the Ph.D. degree in Electronics from the University of California, Berkeley, in 1972. He has been at the Katholieke Universiteit Leuven since 1972, and is now a full Professor of Electrical Engineering. He has held other

academic posts at the University of California, Stanford Uni- versity, the Technical University of Lausanne and the University of Pennsylvania, Philadelphia. His interests are in device model- ling, design of integrated circuits and medical electronics and sensors.

Gaston Vantrappen, born in 1927, obtained a degree of MD at the University of Leuven in 1953, specialised in Internal Medicine from 1953 to 1959 and obtained a Ph.D. at the Uni- versity of Leuven in 1961. He is presently Pro- fessor of Medicine of the University hospitals of Leuven and Head of the Gastroentorologic Research Centre of the University of Leuven. His main research interest is gastrointestinal motility and oesophageal disease.

Jozef Janssens was born in Merksem, Belgium, in 1943. He received his MD degree in Surgery & Obstetrics in 1968 from the Katholieke Universiteit Leuven, Belgium and his Special- isation in Internal Medicine in 1974. He is Adjunct Head of the Hospital St. Raphael- Gasthuisberg, Leuven Lector (since 1978) and Teaching Professor at the Department of Medicine, Katholieke Universiteit Leuven, since 1979.

63