Evaluation of the Wiener filter applied to evoked EMG potentials

Electroencephalograph y and Clinical Neuroph ysiology, 1979, 46:475--478

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© Elsevier/North-Holland Scientific Publishers, Ltd.

EVALUATION OF THE WIENER F I L T E R APPLIED TO EVOKED EMG POTENTIALS R.E. KEARNEY Aviation Medical Research Unit, McGill University, Montreal (Canada)

(Accepted for publication: August 4, 1978)

A number of recent articles have advocated the use of a posteriori Wiener filtering to improve the signal-to-noise (S/N) ratio of time-averaged evoked responses (Walter 1969; Doyle 1975; Hartwell and Erwin 1976). It has been proposed t h a t with this technique adequate estimates of evoked potentials may be obtained with fewer responses than with simple averaging. However, a number of theoretical difficulties with the Wiener filter have also been described (Ungan and Basar 1976; Strackee and Cerri 1977). It is difficult to assess the general importance of these because the performance of the Wiener filter will depend upon the nature of the noise and the evoked potential. Hence, it would appear that the value of the Wiener filter could best be assessed by evaluating its performance in a number of specific applications as suggested by Doyle (1977). We are currently using the Wiener filter to improve the S/N ratio of responses evoked in tonic electromyographic (EMG) activity by cutaneous electrical stimulation. We have evaluated the performance of this filter using a m e t h o d based on t h a t suggested by Doyle (1977). The present report describes the results of this evaluation which indicate that the Wiener filter is extremely valuable in our application.

Methods

Two types of data were used to assess the filter: experimentally observed responses; and

simulated responses generated by adding a known response to noise records. The analysis of the experimental responses was undertaken to assess the performance of the Wiener filter in the actual experimental situation while the use of simulated data allowed a more detailed analysis to be carried out. The experimental responses were those evoked in tonic EMG activity of tibialis anterior by cutaneous electrical stimulation. EMGs were measured with surface electrodes over the belly of the muscle and then high pass filtered (100 Hz cut off), full wave rectified and low pass filtered (500 Hz cut off). The subject maintained a constant level of contraction aided by a meter display of the smoothed and rectified EMG. Stimuli were rectangular voltage pulses applied to the median arch of the foot at a level approximately 3 times the sensory threshold. A computer sampled the EMG at 2000 Hz with 12 bit resolution for 70 msec prior to the stimulus and 180 msec after it. The experimental data consisted of 400 responses to stimuli recorded in one experiment. An additional 400 responses were recorded in the same conditions with no stimulus as a 'sample of the noise. Simulated responses were generated by adding the ensemble average of the 400 experimental responses to each of the noise records. The noise records were scaled to provide the desired S/N ratio. Three sets of simulated data were generated having S/N ratios (in terms of power) of 1, 0.1 and 0.01. Responses were preprocessed to suppress

476

the stimulus artifact and r e m o v e any n o n - z e r o mean value. T h e response was t h e n added to the ensemble average and its s p e c t r u m (estim a t e d t h r o u g h the use o f a H a m m i n g w i n d o w and a discrete F o u r i e r t r a n s f o r m ) a d d e d to the average s p e c t r u m . T h e Wiener coefficients were c o m p u t e d using the e q u a t i o n s given by D o y l e ( 1 9 7 5 ) e x c e p t t h a t coefficients less t h a n zero were set t o zero to p r e v e n t the addition o f spurious noise b y the filter. T h e a c c u r a c y o f the ensemble average and Wiener filter estimates o f the e v o k e d potentials was assessed b y c o m p u t i n g the m e a n square e r r o r b e t w e e n the estimate and the 'actual' response. T h e 'actual' response was t a k e n as the average o f 400 responses for the e x p e r i m e n t a l d a t a while for the simulated data it was simply the response which had been a d d e d to the noise records. T h e ratio o f the mean square e r r o r o f the Wiener filter estimate t o t h a t o f the ensemble average estim a t e was used as a figure o f merit for the Wiener filter. This is the same as D o y l e ' s R measure ( D o y l e 1977).

Results T h e Wiener filter p r o v e d t o be very effective when applied to the e x p e r i m e n t a l data as d e m o n s t r a t e d in Fig. 1 which shows the ensemble average after 10 responses (A), the Wiener filter estimate a f t e r 10 responses (B) and the ensemble average after 400 responses (C). By e x a m i n a t i o n , the Wiener filter estimate m a y be seen to be closer t o the final ensemble average t h a n was the ensemble average estimate. T h e effectiveness o f the filter is f u r t h e r illustrated by the decreased noise in the pre-stimulus p o r t i o n o f the response to the left o f the d o t t e d line. The effectiveness o f Wiener filtering is expressed quantitatively in Fig. 2A which plots the figure o f merit for the Wiener filter as a function o f the n u m b e r o f responses (N). It was higher for low N t h a n for large N b u t was always greater t h a n one indicating t h a t Wiener filtering c o n s i s t e n t l y p r o v i d e d a b e t t e r

R.E. K E A R N E Y A

,li't

C

~v

f

SO ms

Fig. 1. Effects o f Wiener filtering o f e x p e r i m e n t a l data. A: e n s e m b l e average estimate a f t e r 10 responses. B: Wiener filtered e s t i m a t e a f t e r 10 responses. C: e n s e m b l e average e s t i m a t e a f t e r 4 0 0 responses. T h e o n s e t o f t h e s t i m u l u s is i n d i c a t e d b y t h e d o t t e d line.

estimate o f the final average t h a n simple ensemble averaging. A m o r e extensive analysis o f the simulated data was possible since b o t h the e v o k e d p o t e n t i a l and the S/N ratio were k n o w n . The results o f this s t u d y are s u m m a r i z e d in Fig. 2B which shows the figure o f merit for the Wiener filter as a f u n c t i o n o f N for 3 S/N ratios. N o t e t h a t the figure o f m e r i t was again higher for low N t h a n for large N, and it was higher for low S/N ratios than for high b u t was always greater t h a n one. An i m p o r t a n t advantage o f Wiener filtering is its ability to r e d u c e the n u m b e r o f responses required to obtain a good estimate o f an e v o k e d potential. This is d e m o n s t r a t e d in Table I which gives the n u m b e r o f responses required for the Wiener filter and ensemble average estimates to reach a specified mean square error for simulated data having an S/N ratio o f 0.01. N o t e t h a t the Wiener filter required significantly f e w e r responses t o obtain a given e r r o r t h a n did the ensemble average. T h e i m p r o v e m e n t ranged

477

EVALUATION OF THE WIENER FILTER ,4,

from a factor of more than 4 at low N to less than 2 for large N.

3"

Discussion

(R}

NU~ER OF RESPONSES

SIGNAL TO NOISE RATIO A

F

\

G

~

E

=

I 00

D =010

\

v =001

E I T

•

(R) I]

/ NUM~}ER OF RESPONSES

Fig. 2. Figure o f m e r i t as a f u n c t i o n o f n u m b e r o f responses for the W i e n e r filter applied to (A) experimental d a t a a n d (B) simulated data with 3 signal-ton o i s e ratios.

Summary

TABLE I N u m b e r o f r e s p o n s e s r e q u i r e d for the ensemble average and Wiener filter e s t i m a t e s t o r e a c h a specified e r r o r for s i m u l a t e d d a t a w i t h a signal-to-noise r a t i o o f 0.01. Error

9000 8000 7000 6000 5000 4000 3000 2000

The results of this study indicate that Wiener filtering is an extremely valuable tool for the study of evoked EMG potentials since it provides a better estimate (in the sense of mean square error) than does simple ensemble averaging. As a consequence, it reduces the number of responses required to obtain a good estimate of the response. The filter appears to be most effective in cases where the S/N ratio is l o w e s t - that is after a few responses and in cases where there is much noise. This is to be expected since if there is not much noise in the records a filter is n o t going to be able to bring about much improvement. It should be noted that the results of this study may not be applicable to other situations. The effectiveness of the filter will depend upon the spectra both of the noise and of the evoked potential in any given situation. Hence it is suggested that an evaluation of the performance of the Wiener filter should be carried out whenever a new application of the technique is undertaken.

NE

NW

(ensemble

(Wiener

average)

filter )

40 50 60 75 110 140 175 260

10 15 20 25 30 50 60 150

Ratio

4 3.3 3 3 3.7 2.8 2.9 1.7

The application of the Wiener filter to the estimation of responses evoked in the tonic EMG activity of tibialis anterior by cutaneous electrical stimulation of the foot is described. The effectiveness of the filter is assessed using both experimental and simulated data by computing the mean square error between the actual evoked potential and ensemble average and Wiener filter estimates of it. The Wiener filter is shown to provide a better estimate of the final response than simple ensemble averaging. The improvement is most marked in cases where the signal-to-noise ratio is small, but the Wiener filter estimate is always

478 b e t t e r t h a n the ensemble average estimate. It is c o n c l u d e d t h a t Wiener filtering significantly reduces the n u m b e r o f responses required to obtain a g o o d estimate o f t h e e v o k e d p o t e n t i a l in this e x p e r i m e n t a l situation.

R.E. KEARNEY d ' u n e b o n n e e s t i m a t i o n de la r6ponse 6voqu6e dans c e t t e situation e x p 6 r i m e n t a l e . This work was supported by a grant from the Canadian Medical Research Council (Grant No. MA 6101).

R6sum6 References

Evaluation du filtre de Wiener appliqud aux rdponses EMG dvoqudes L ' a u t e u r d6crit l'application du filtre de Wiener ~ la mesure des r6ponses de l'activit6 EMG t o n i q u e du muscle j a m b i e r ant6rieur, 6voqu6es par stimulation 61ectrique cutan6e du pied. L'efficacit6 de ce filtre est v6rifi6e partir de donn6es exp~rimentales et simul6es en calculant le carr6 m o y e n de l'erreur entre le p o t e n t i e l 6voqu6 r6el, le m o y e n n a g e de tous les potentiels, et celui qui est appr6ci6 au m o y e n d u filtre de Wiener. Le filtre de Wiener s'av6re f o u r n i r u n e e s t i m a t i o n de la r6ponse finale meilleure que le simple m o y e n n a g e . Cette am61ioration est d ' a u t a n t plus n e t t e que le r a p p o r t signal sur bruit est faible, mais l'estimation par filtre de Wiener est t o u j o u r s meilleure que l'estimation par m o y e n n a g e . L ' a u t e u r c o n c l u t que le illtrage Wiener r6duit de faqon significative le n o m b r e de p o t e n t i e l s n6cessaires ~ l ' o b t e n t i o n

Doyle, D.J. Some comments on the use of Wiener filtering for the estimation of evoked potentials. Electroenceph. clin. Neurophysiol., 1975, 38: 533--534. Doyle, D.J. A proposed methodology for evaluation of the Wiener filtering method of evoked potential estimation. Electroeneeph. elin. Neurophysiol., 1977, 43: 749--751. HartweI], J.W. and Erwin, C.W. Evoked potential analysis: on-line signal optimization using a minicomputer. Electroenceph. clin. Neurophysio]., 1976, 41: 416--421. Strackee, J. and Cerri, S.A. Some statistical aspects of digital Wiener filtering and detection of prescribed frequency components in time averaging of biological signals. Biol. Cybernet., 1977, 28: 55--61. Ungan, P. and Basar, E. Comparison of Wiener filtering and selective averaging of evoked potentials. Electroenceph. clin. Neurophysiol., 1976, 40: 516--520.

Walter, D.O. A posteriori 'Wiener filtering' of average evoked responses. Electroenceph. physiol., 1969, SuppL 27: 61--70.

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