Simplified Optimal Estimation of Time-Varying Electromyogram Standard Deviation (EMGσ): Evaluation on Two Datasets.

To facilitate the broader use of EMG signal whitening, we studied four whitening procedures of various complexities, as well as the roles of sampling rate and noise correction. We separately analyzed force-varying and constant-force contractions from 64 subjects who completed constant-posture tasks about the elbow over a range of forces from 0% to 50% maximum voluntary contraction (MVC). From the constant-force tasks, we found that noise correction via the root difference of squares (RDS) method consistently reduced EMG recording noise, often by a factor of 5-10. All other primary results were from the force-varying contractions. Sampling at 4096 Hz provided small and statistically significant improvements over sampling at 2048 Hz (~3%), which, in turn, provided small improvements over sampling at 1024 Hz (~4%). In comparing equivalent processing variants at a sampling rate of 4096 Hz, whitening filters calibrated to the EMG spectrum of each subject generally performed best (4.74% MVC EMG-force error), followed by one universal whitening filter for all subjects (4.83% MVC error), followed by a high-pass filter whitening method (4.89% MVC error) and then a first difference whitening filter (4.91% MVC error)-but none of these statistically differed. Each did significantly improve from EMG-force error without whitening (5.55% MVC). The first difference is an excellent whitening option over this range of contraction forces since no calibration or algorithm decisions are required.

Simplified Optimal Estimation of Time-Varying Electromyogram Standard Deviation (EMGσ).

Previous works have shown that whitening improves the processed electromyogram (EMG) signal for use in end applications such as EMG to torque modelling. Traditional whitening methods fit each subject from calibration contractions, which is a hindrance to their widespread use. To eliminate this cumbersome calibration, a universal whitening filter was developed using the whitening filters from a pre-existing data set (64 subjects, 8 electrodes/subject). Since the shape of each subject-specific whitening filter was observed to be relatively consistent across subjects, the universal whitening filter was formed as their ensemble average. The processed EMG was then used to model surface EMG to torque about the elbow. Traditional and universal whitening provided the same EMG-torque benefit, each improving statistically over unwhitened processing by ~14% during dynamic contractions. We further studied the use of root difference of squares (RDS) post-processing to attenuate additive measurement noise in EMG channels. With and without whitening, RDS processing (vs. no RDS processing) better attenuated additive noise, reducing it from 2-4% (on average) of the processed EMG from a 50% contraction down to < 1%. The combined use of universal whitening filters and RDS processing should be a particular benefit in real-time applications such as prosthesis control.

Optimal Estimation of EMG Standard Deviation (EMG σ ) in Additive Measurement Noise: Model-Based Derivations and Their Implications.

Typical electromyogram (EMG) processors estimate EMG signal standard deviation (EMG σ ) via moving average root mean square (RMS) or mean absolute value (MAV) filters, whose outputs are used in force estimation, prosthesis/orthosis control, etc. In the inevitable presence of additive measurement noise, some processors subtract the noise standard deviation from EMG RMS (or MAV). Others compute a root difference of squares (RDS)-subtract the noise variance from the square of EMG RMS (or MAV), all followed by taking the square root. Herein, we model EMG as an amplitude-modulated random process in additive measurement noise. Assuming a Gaussian (or, separately, Laplacian) distribution, we derive analytically that the maximum likelihood estimate of EMG σ requires RDS processing. Whenever that subtraction would provide a negative-valued result, we show that EMG σ should be set to zero. Our theoretical models further show that during rest, approximately 50% of EMG σ estimates are non-zero. This result is problematic when EMG σ is used for real-time control, explaining the common use of additional thresholding. We tested our model results experimentally using biceps and triceps EMG from 64 subjects. Experimental results closely followed the Gaussian model. We conclude that EMG processors should use RDS processing and not noise standard deviation subtraction.