IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 45, NO. 6, JUNE Hogan and Mann [3], [4] actually present this square root formula as

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1 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 45, NO. 6, JUNE Communications Influence of Smoothing Window Length on Electromyogram Amplitude Estimates Yves St-Amant, Denis Rancourt, and Edward A. Clancy* Abstract A systematic, experimental study of the influence of smoothing window length on the signal-to-noise ratio (SNR) of electromyogram (EMG) amplitude estimates is described. Surface EMG waveforms were sampled during nonfatiguing, constant-force, constant-angle contractions of the biceps or triceps muscles, over the range of 10% 75% maximum voluntary contraction. EMG amplitude estimates were computed with eight different EMG processor schemes using smoothing length durations spanning ms. An SNR was computed from each amplitude estimate (deviations about the mean value of the estimate were considered as noise). Over these window lengths, average 6 standard deviation SNR s ranged from to for unwhitened single-channel EMG processing and from to for whitened, multiplechannel EMG processing (results pooled across contraction level). It was found that SNR increased with window length in a square root fashion. The shape of this relationship was consistent with classic theoretical predictions, however none of the processors achieved the absolute performance level predicted by the theory. These results are useful in selecting the length of the smoothing window in traditional surface EMG studies. In addition, this study should contribute to the development of EMG processors which dynamically tune the smoothing window length when the EMG amplitude is time varying. Index Terms Biological system modeling, electromyography, EMG amplitude estimation, modeling, whitening. I. INTRODUCTION The amplitude of the surface electromyogram (EMG) waveform has been used as a noninvasive tool for assessing the degree of muscular exertion (e.g., as the command input of EMG-controlled prosthetic limbs), and is being investigated as an indicator of the force developed by the muscles. Classical methods for processing the EMG waveform (e.g., signal rectification followed by low-pass filtering [1]) provide a processed EMG amplitude which is inherently noisy. For constant-force, constant-angle, nonfatiguing muscular contraction, the signal-to-noise ratio (SNR) of EMG amplitude estimates (defined as the sample mean of the estimate divided by its sample standard deviation) using root-mean-square (RMS) detection has been shown theoretically to be related to the statistical bandwidth [2] of the EMG signal (B s, in Hz), the number of EMG channels recorded on a muscle (L), and the length of the Manuscript received July 7, 1997; revised December 10, This work was supported in part by National Institutes of Health under Grant AR40029, in part by the United States Department of Education under NIDRR Grant H133E80024, and in part by the Conseil de Recherche en Sciences Naturelles et en Génie du Canada. Asterisk indicates corresponding author. Y. St-Amant and D. Rancourt ( boloria@gmc.ulaval.ca) are with the Mechanical Engineering Department, Laval University, Québec, P.Q., Canada G1K 7P4. *E. A. Clancy is with the Liberty Mutual Research Center for Safety and Health, 71 Frankland Road, Hopkinton, MA USA ( msmail5.clancye@tsod.lmig.com). Publisher Item Identifier S (98) smoothing window (T, in seconds) applied to the data as 1 [4] SNR = p 2 1 2B s 1 L 1 T: (1) (This formula assumes that each EMG channel has the same statistical bandwidth.) Note that for sampled data, T = N=f, where N is the number of samples in the smoothing window and f is the sampling frequency in Hz. The larger the SNR, the better the EMG amplitude estimate. Investigators have looked at experimental and theoretical methods to improve the SNR by increasing the signal bandwidth (i.e., applying whitening filters to the EMG waveform) [3] [9] and the number of EMG channels [3], [4], [6], [10] [12] contributing to an amplitude estimate. Limited attention, however, has been focused on determining experimentally the role of smoothing window length on the SNR. Inman et al. [1] examined three time constants ( = 100, 200, 250 ms) with their original analog processor (a full-wave rectifier followed by a resistor-capacitor low-pass filter). Qualitative performance results were shown, but no quantitative SNR results were given. Kreifeldt [13] investigated the SNR for three settling times (250, 500, 1000 ms) from three analog smoothing circuits (first-order Butterworth, third-order Butterworth, and third-order averaging filters) at four constant-force, constant-angle contraction levels [5%, 10%, 25%, and 50% maximum voluntary contraction ()]. Because contraction durations were between 40 and 60 s, it is likely that some of the contractions (particularly those at higher levels) were fatiguing. Their results showed that increasing the settling time increased the SNR. Thusneyapan and Zahalak [12] examined four cutoff frequencies (5, 10, 20, and 30 Hz) with a nine-channel analog processor which performed analog rectification, combination and low-pass (second-order Butterworth) filtering. For EMG amplitude estimates, the SNR ranged from 4.6 (with the 30 Hz cutoff frequency) to 6.9 (with the 5-Hz cutoff frequency). 2 Taken together, these prior investigations certainly demonstrate that the SNR increases with the smoothing window length for constantforce, constant-angle, nonfatiguing contractions. However, processors which increase the statistical bandwidth of the EMG signal by including whitening filters (single or multiple channel) have not been investigated. In addition, and most importantly, the data are too sparse to validate the fit of an analytical function such as the theoretical square root relationship of Hogan and Mann [4]. Use of an analytical function to represent the variation of the SNR with window length is mathematically convenient for the optimization process of dynamic EMG adaptive window length processors. In this case, higher fidelity EMG amplitude estimates can be achieved if the window length is tuned throughout the duration of a contraction [7], [14] [18]. Basically, a tradeoff is maintained between error due to estimator variance (which is diminished via a long smoothing window) and error due to estimator bias (which is diminished in the dynamic case 1 Hogan and Mann [3], [4] actually present this square root formula as a simplification/approximation of the true SNR formula. We compared the square root formula to the true formula using MATLAB (version 4.0). For values of 2B s 1 L 1 T over the range of 12 to the two formulas never differ by more than 0.05 and the percentage difference is always less than 1%. The difference drops rapidly as 2Bs 1 L 1 T increases. Thus, for all intents and purposes, the square root formula given here can be considered equivalent to the more complex formula found in [3]. 2 These result values have been approximated from a graph in [12], since the actual values are not found in the text /98$ IEEE

2 796 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 45, NO. 6, JUNE 1998 with a short smoothing window). Previous authors [7], [14], [17] have shown that this tradeoff can be written mathematically as: MSE = b 2 + 2, where MSE is the mean square error in the EMG amplitude estimate, b is the bias error and 2 is the variance error. Since the variance represents the purely stochastic portion of the error, it is related to the SNR in (1) as: SNR = s 2 = 2, where s is the EMG amplitude estimate (e.g., from mean-absolute-value (MAV) or RMS processing) and is the standard deviation of the estimate. Hence, establishing the experimental relationship between SNR and window length in the constant-force, constant-angle, nonfatiguing situation has direct bearing on EMG processing for dynamic situations. This report provides such evaluation. A preliminary report of this work appeared in [19]. II. EXPERIMENTAL STUDY A. Experimental Apparatus and Methods The experimental apparatus and methods have been described in detail elsewhere [9], [11], [20]. Briefly, a chair was instrumented to measure the torque generated about the elbow. The subject was seated and secured into a straight-back chair via five quick-release belts. The subject s right arm was oriented so that the upper arm and forearm were in the plane parallel to the floor (shoulder abducted 90 from the anatomic position), the forearm was oriented in the parasagittal plane, with the wrist in complete supination, and the elbow flexion angle was about 90. The subject s right wrist was mounted, via a wrist cuff, to a cantilever beam. The torque produced by the elbow was measured by a complete strain gauge Wheatstone bridge affixed on the beam. Eight commercial electrode-amplifiers (Liberty Mutual MYO111 [21] with a second-order Hz bandpass filter) were placed in-line, side-by-side, transversely across the flexor (biceps brachii) or extensor (triceps) muscles of the elbow. The two electrode contacts of each electrode-amplifier were oriented along the long axis of the upper arm (i.e., oriented along the assumed direction of action potential conduction). The electrode-amplifiers were located approximately midway between the elbow and the midpoint of the upper arm, clustered about the muscle midline. Each electrode-amplifier consisted of a pair of 4-mm diameter, stainlesssteel, hemispherical electrode contacts separated by a distance of 15 mm (center to center). The center-to-center distance between adjacent electrode-amplifiers was approximately 1.75 cm. Five subjects (four male and one female, ranging in age from 23 to 37 years), with no known neuromuscular deficits of the right shoulder, arm or hand, participated in the experiment. Informed consent was received from each subject. Two subjects were studied during an elbow flexion task, three were studied during an elbow extension task. During an experimental trial, the output voltage of the strain gauge circuit and a target torque level were presented as the two displays of a dual-trace oscilloscope. The subject was instructed to begin at rest, then gradually increase flexion/extension torque until the target torque level was achieved (typically over a period of s). The subject maintained the target torque level until a 5-s segment of data was recorded. Two initial 3-s trials were averaged to provide a rough estimate of the strain gauge circuit output voltage corresponding to. A sequence of five sets of constant-force, constant-angle contractions was then conducted. Each set consisted of four trials, one trial each at 10%, 25%, 50%, and 75%. Trials within a set were randomized. A rest period of 2 min between trials (3 min after 100% trials) was provided to prevent fatigue [22]. EMG and strain gauge circuit output data were sampled at 2048 Hz, using a 12-bit A/D converter, and processed off-line. Each data record was plotted and visually inspected. Due to the high gain (3600) of the electrode-amplifiers, some electrode-amplifiers saturated during some experiments. All data from any electrode-amplifier from a given subject which saturated during any portion of any record were discarded from further analysis. A total of 100 multiple site recordings, comprised of 660 single site recordings, were available for analysis. Previous experimental studies based on the data from these trials are described in [9] and [11]. B. Methods of Analysis The SNR versus smoothing window length relation was studied with unwhitened/whitened single/multiple channel EMG processors which used MAV/RMS detectors. Thus, eight EMG amplitude processors were formed. As a preprocessing step, the sample-mean value of each 5-s EMG waveform was subtracted from the waveform. This step provided a simple method for removal of individual channel offsets due to the A/D converter and front-end electronics. The mean-adjusted waveform samples were then used to form the eight processors as follows. 1) A single channel unwhitened amplitude processor was formed as the simple RMS detector. 2) A single channel whitened processor was formed by temporally whitening each data record, followed by RMS detection (see [9], [11], and [20] for details of the whitening technique). Briefly, a fourth-order moving average whitening filter was constructed for each electrode-amplifier for each subject, and applied to all trials recorded by that electrode-amplifier. For each subject, a whitening filter was calibrated by averaging the autoregressive (AR) power spectrum coefficients computed from each 50% trial. The whitening filter model order and choice of 50% as the calibration contraction were selected based on prior investigation conducted on these data [9]. 3) A multiple channel (four channel) unwhitened amplitude processor was formed by equalizing (normalizing to a value of one) the variance of each channel (based on the average variance of the five 50% trials), and then performing spatial-temporal RMS detection. If the multiple channel EMG waveforms (after variance equalizing) at sample k are denoted m l (k) and the channel index l ranges from one to L = 4, then spatial-temporal RMS detection to form this EMG amplitude estimate is written as ^s 3(k) = 1 N1L L l=1 k i=k0n+1 m2 l (i) 1=2. 4) A multiple channel (four channel) whitened amplitude processor was formed by temporally whitening each channel (which inherently normalizes the variance of each channel), and then performing spatial-temporal RMS detection. Whitening filters were the same as in the single channel case. Spatial uncorrelation was not performed, since, based on prior work [11], [20] it provided little performance improvement with this electrode arrangement. 5 8) These processors parallel the above processors, except that RMS detection is replaced with MAV detection. For each processor, the smoothing window length was varied from a minimum value of five samples (2.45 ms) to a maximum value of 1024 samples (500 ms). SNR s of each EMG amplitude were computed as the square root of the ratio of the squared amplitude estimate sample mean divided by the amplitude estimate sample variance. To avoid start-up transients, the first = 1029 samples of each amplitude estimate were discarded prior to computing the SNR. All computation was performed using MATLAB (version 4.0) on an IBM-compatible PC.

3 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 45, NO. 6, JUNE Fig. 1. Effect of smoothing window length on the SNR (data pooled across subjects and force levels). Mean SNR s are shown for the eight processors. Lines are an aid to the eye only. One-sided error bars show the standard deviations for the MAV processors. (Standard deviations for the RMS processors are similar.) Inset table tabulates the mean 6 standard deviation SNR s for the MAV processors. III. EXPERIMENTAL RESULTS The aim of this study was to obtain a more complete picture of the SNR variation over a practical range of window lengths. The SNR performance for the eight processors is shown in Fig. 1. Data from all contraction levels and all subjects were pooled together. Hence, results for single channel processors are derived from 660 SNR s, while those for multiple channel processors are derived from 100 SNR s. Using a 245-ms smoothing window, Clancy and Hogan [9], [11] showed that the SNR curves perform differently from one processor to another. Our results show that this difference appears to be true for any of the window lengths that were studied. Both whitening and spatio-temporal techniques seemed to improve the SNR performance, and MAV processors consistently produced equal or higher SNR values than RMS processors. A more detailed analysis of the SNR variation was conducted by grouping data by subject or by contraction level. Grouping data by subject showed that only one subject had generally higher SNR values than the others, and all five subjects still exhibited a square root behavior. The SNR curves for all contraction levels are shown in Fig. 2. The curves suggest that the SNR performance decreases with contraction level, but all curves still exhibit a square root behavior. In order to provide statistical power to the previous observations, a multivariate analysis of variance (ANOVA) (with =0:05) was performed using SAS, version 6.09 (SAS Institute Inc., Cary, NC). The analysis was performed after applying a logarithmic transformation to the SNR data. This particular transformation was chosen to satisfy the hypothesis of homogeneous variance required by the statistical analysis. Following this transformation, it was found that the residuals of the fitted models were distributed uniformly. Nonparametric tests on the logarithm of the SNR were initially performed because what might be true at a given window length may not be so at another. The tests were conducted at only two different window lengths: T = 30 ms and T = 500 ms. Results being generally similar, we pursued the statistical analysis using a parametric test where the SNR curves (as a function of smoothing window length) were least-squares fitted to the following model: ln(snr) = ln(2 1 2B s 1 L 1 T ) b = b 1 ln(2 1 2B s 1 L) +b 1 ln T = b 0 + b 1 ln T: This model is a more generalized form of (1). The influence of different factors on the SNR was then analyzed using both b 0 and b 1 variations. Values for b 0 and b 1 are given in Table I, for the four contraction levels, for all eight processors. The analysis of variance test on all the data showed that there were significant interactions between subjects, force levels and processors. Further analysis of variations across subjects was not of interest and, thus, was not pursued. Statistical tests showed that b 1 was significantly different from zero, hence supporting the observation that the SNR varies with window length. In addition, all processors, at all contraction levels, have a b 1 close to 0.5, indicating a square root relationship between SNR and window length. Both parameters, b 0 and b 1, were ordered and statistical comparisons were performed using a Tukey (LSD) comparison test, with = 0:05. Statistical analysis of the data

4 798 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 45, NO. 6, JUNE 1998 Fig. 2. Influence of contraction force level on SNR (data pooled across subjects). Mean SNR s (and one-sided standard deviations) are shown. Lines are an aid to the eye only. In all cases, EMG processing uses MAV detection and four whitened channels. Each entry is averaged across 25 SNR s. Inset table tabulates the mean 6 standard deviation SNR s shown in the plots. TABLE I FITTING COEFFICIENTS b0 AND b1 FOR THE FOUR CONTRACTION LEVELS, FOR THE EIGHT PROCESSORS Processor 10% b0 25% 50% 75% 10% 25% b1 50% 75% MAV, unwhite, single MAV, unwhite, multiple MAV, white, single MAV, white, multiple RMS, unwhite, single RMS, unwhite, multiple RMS, white, single RMS, white, multiple The coefficients fit the model: (SNR), where SNR is the signal-to-noise ratio and is the smoothing window length (in seconds). confirmed that: 1) whitening improves the SNR performance (increase of b0), 2) multiple channel combination improves the performance in a similar manner, 3) both techniques together help even more, and 4) MAV processors, although always ranked higher than RMS, are not statistically different than the RMS. This last result suggests that MAV processors which often have easier and faster realizations in both analog and digital systems can be successfully substituted for the theoretically prescribed RMS processors. Results showed that both fitting parameters b0 and b1 decrease with increasing force level, and hence the SNR. In the global parametric analysis, the variation of b1 was ranked using a Tukey (LSD) comparison test ( =0:05). Adjacent levels 10% versus 25%, 25% versus 50%, and 50% versus 75% could not be distinguished statistically. However, levels 50% and 75% each differed significantly from 10%. IV. DISCUSSION A. SNR Square Root Relationship As predicted by the theoretical work of Hogan and Mann [3], [4], the SNR performance generally exhibited a square root behavior with respect to window length, since the b1 values were close to 0.5. However, none of the processors achieved the level of performance specified by the theory. Therefore, adaptive window length EMG amplitude estimators which use this theoretical model may underestimate the variance component of the error. For example,

5 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 45, NO. 6, JUNE TABLE II FITTING FACTOR c AND AVERAGE ERRORS (BETWEEN THE FIT AND EXPERIMENTAL DATA) FOR ALL EIGHT PROCESSORS Processor Fitting factor "c" Mean error MAV, unwhite, single MAV, unwhite, multiple MAV, white, single MAV, white, multiple RMS, unwhite, single RMS, unwhite, multiple RMS, white, single RMS, white, multiple The factor fits the model: SNR, where SNR is the experimentally adjusted signal-to-noise ratio and is the smoothing window length (in seconds). a multiple channel, whitened, RMS processor (i.e., L =4;B s = 1024 Hz) has a theoretical SNR versus T relationship of SNR L=4;B =1024 Hz = p T: Thus, for T =200 ms, the theoretically predicted SNR value is Fig. 1 shows that this performance level is not achieved the actual average SNR is 24.5 (with the MAV detector). Further, experimentally achieved performance seems to be consistently below the theoretical prediction. Not all of the statistical degrees of freedom modeled in the theoretical analysis have been recovered from the experimental data. This observation was explored by least-squares fitting the SNR versus T relationship to an experimentally adjusted (EA) square root model; SNR EA = p c 1 T, where c is a multiplicative factor representing the theoretical factor 2 1 2B s1l. The fitting factors (and fit errors) for all eight processors are tabulated in Table II. In general, the fit is quite good. These fitting factors can be used to more accurately represent the experimentally achieved SNR versus T relationship for the eight EMG processors studied. At least two reasons for the poorer experimental performance (compared to the theoretical model) can be postulated. First, the theory does not model measurement noise in the electrode recording when, in fact, such noise clearly exists. This noise would likely decrease the performance of any EMG amplitude processor. Second, the theoretical model is based on the assumption that the EMG waveform samples are distributed as a Gaussian random process. However, a recent analysis of the data used in this study suggests that these recordings are more closely represented as a Laplacian random process. Further, theoretical and simulation analysis of MAV and RMS processing of Laplacian data showed that the predicted SNR of the amplitude estimate is considerably reduced (by 30%) [23]. Hence, minor variations in the density function of the sampled data can have a large influence on the achieved SNR. B. Influence of Contraction Level The results indicated that experimental SNR decreased as the contraction level increased. Although no definitive reason for this observation can be provided, two possibilities will be discussed. First, note that high-frequency (14 Hz) periodic oscillations were found superimposed on the force recordings during the 50% and 75% s. These oscillations seemed to be due to normal tremor activity associated with the high force output of the muscles. With tremor activity during high contractions, muscle activation deviated, in part, from a constant-force contraction, and likely hindered the achieved SNR. Second, actual changes in the physiologic EMG spectrum may occur as a function of contraction level. As contraction force increases, motor unit recruitment and firing rates increase, perhaps introducing systematic differences in the EMG bandwidth (and, thus, the SNR). C. Whitening at Low Contraction Levels As expected from (1) and prior experimental work [3] [9], increasing the signal bandwidth (B s) via whitening generally improved SNR performance. From Fig. 1 it would appear that whitening always provides a processing benefit. This is not necessarily the case. Initial evaluation of whitening filters calibrated with a 50% trial, then applied to data recorded during contractions at less than 10% (a situation not investigated in this report) provided poor results [9], [20]. An additive background noise was found superimposed on the EMG signal, e.g., a nonzero EMG amplitude was noted when the subjects were asked to fully relax their muscles. At low EMG amplitude, this additive background noise (not included in classical EMG models) seemed to dominate the output of the whitening filters. The relative contribution of background noise to the EMG amplitude estimates seemed to increase progressively as the EMG amplitude decreased. Similar difficulties have been noted by Kaiser and Peterson [5]. The use of adaptive whitening filters, which tune the shape of the whitening filter as a function of the EMG amplitude, offers a promising solution to this problem [5], [20]. V. SUMMARY AND CONCLUSIONS This study has demonstrated that a simple square root formula can be used to represent the experimental SNR performance of eight different EMG estimators. An exhaustive mapping of the SNR performance versus window length was obtained for the EMG estimators. Both whitening and spatio-temporal techniques improved SNR performance, and MAV processors consistently produced equal or higher SNR values than RMS processors. It was also found that SNR performance decreased with increasing contraction level. The results of this study can be used to select an appropriate smoothing window length in traditional surface EMG studies. In addition, the results of this study can be used to develop adaptive window length EMG processors in which the length of the smoothing window is dynamically tuned when the EMG amplitude is time varying. ACKNOWLEDGMENT Experimental data for this study were collected at the Eric P. and Evelyn E. Newman Laboratory for Biomechanics and Human Rehabilitation at the Massachusetts Institute of Technology, Cambridge. The authors would like to thank N. Plante of the Statistics Consulting Service, Department of Mathematics and Statistics, Laval University, Québec, Canada, for serving as a statistical consultant to this project. REFERENCES [1] V. T. Inman, H. J. Ralston, J. B. de C. M. Saunders, B. Feinstein, and E. W. Wright, Relation of human electromyogram to muscular tension, EEG Clin. Neurophysiol., vol. 4, pp , [2] J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures. New York: Wiley, [3] N. Hogan and R. W. Mann, Myoelectric signal processing: Optimal estimation applied to electromyography Part I: Derivation of the optimal myoprocessor, IEEE Trans. Biomed. Eng., vol. BME-27, pp , [4], Myoelectric signal processing: Optimal estimation applied to electromyography Part II: Experimental demonstration of optimal myoprocessor performance, IEEE Trans. Biomed. 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6 800 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 45, NO. 6, JUNE 1998 [6] M. I. A. Harba and P. A. Lynn, Optimizing the acquisition and processing of surface electromyographic signals, J. Biomed. Eng., vol. 3, pp , [7] T. D Alessio, Some results on the optimization of a digital processor for surface EMG signals, Electromyogr. Clin. Neurophysiol., vol. 24, pp , [8] G. C. Filligoi and P. Mandarini, Some theoretic results on a digital EMG signal processor, IEEE Trans. Biomed. Eng., vol. BME-31, pp , [9] E. A. Clancy and N. Hogan, Single site electromyograph amplitude estimation, IEEE Trans. Biomed. Eng., vol. 41, pp , [10] W. R. Murray and W. D. Rolph, An optimal real-time digital processor for the electric activity of muscle, Med. Instrum., vol. 19, pp , [11] E. A. Clancy and N. Hogan, Multiple site electromyograph amplitude estimation, IEEE Trans. Biomed. Eng., vol. 42, pp , [12] S. Thusneyapan and G. I. 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Ghaleb Abstract We consider the problem of detecting visual evoked potentials (VEP s). A matched subspace filter is applied to the detection of the VEP and is demonstrated to perform better than a number of other evoked potential detectors. Unlike single-harmonic detectors, the matched subspace filter (MSF) detector is suitable for detecting multiharmonic VEP s. Moreover, the MSF is optimal in the uniformly most powerful sense for multiharmonic signals with unknown noise variance. Index Terms Detection, evoked potentials, prewhitening, visual acuity. I. BACKGROUND Visual grating acuity (GA) is useful in the clinical evaluation of patients with eye and neurologic disease. GA is obtained by having the subject view a contrast grating at a fixed contrast (usually 100%) while the spatial frequency is increased until the subject can no longer detect the contrast grating. In adults, measurements can be accomplished psychophysically; however, infants, young children, and nonverbal patients cannot be studied with psychophysical methods. Several researchers have proposed using the steady-state visual evoked potential (VEP) as an objective method of determining GA [1] [3]. Most of these methods utilize the second harmonic of stimulus contrast reversal frequency to detect the presence of a VEP. The generalized T 2 statistic [4], the T 2 circ statistic [5], [6], and the Rayleigh phase criterion (RPC) [7], are representative of these types of detection algorithms. All of the above statistics are parametric in the sense that they assume that under the null hypothesis, the noise [electroencephalogram (EEG)] has a Gaussian density. This assumption has been found to be reasonable by several investigators [8], [9]. The record orthogonality test by permutation (ROTP) detector looks at the power in ensemble averages derived via all possible sign permutations of the data frames. If the average corresponding to all + signs (i.e., no sign changes) is in the top 5% of all possible ensemble average powers, a detection is made, hence this detector is nonparametric [10]. Victor and Mast compared the RPC, T 2, and T 2 circ statistics and found that their T 2 circ statistic outperformed the others [5]. One drawback of all of these statistics is that they are all based on the second harmonic of the contrast reversal frequency; there is no reason to expect near-threshold evoked potentials (EP s) to contain only the second harmonic, and if other signal harmonics are present, then current methodology does not appear to have exploited them. Manuscript received November 20, 1996; revised January 13, This work was supported in part by a grant from the Whitaker Foundation, in part by the National Science Foundation under Grant BCS , and in part by an unrestricted grant from Research to Prevent Blindness, Inc. Asterisk indicates corresponding author. *C. E. Davila is with the Electrical Engineering Department, Southern Methodist University, P. O. Box , Dallas, TX USA ( cd@seas.smu.edu). R. Srebro is with the Departments of Ophthalmology and Biomedical Engineering, University of Texas Southwestern, Medical Center, Dallas, TX USA. I. A. Ghaleb is with the Electrical Engineering Department, Southern Methodist University, Dallas, TX USA. Publisher Item Identifier S (98) /98$ IEEE