Probability density of the surface electromyogram and its relation to amplitude detectors

Abstract—When the surface electromyogram (EMG) generated from constant-force, constant-angle, nonfatiguing contractions is modeled as a random process, its density is typically assumed to be Gaussian. This assumption leads to root-mean-square (RMS) processing as the maximum likelihood estimator of the EMG amplitude (where EMG amplitude is defined as the standard deviation of the random process). Contrary to this theoretical formulation, experimental work has found the signal-to-noise-ratio [(SNR), defined as the mean of the amplitude estimate divided by its standard deviation] using mean-absolute-value (MAV) processing to be superior to RMS. This paper reviews RMS processing with the Gaussian model and then derives the expected (inferior) SNR performance of MAV processing with the Gaussian model. Next, a new model for the surface EMG signal, using a Laplacian density, is presented. It is shown that the MAV processor is the maximum likelihood estimator of the EMG amplitude for the Laplacian model. SNR performance based on a Laplacian model is predicted to be inferior to that of the Gaussian model by approximately 32%. Thus, minor variations in the probability distribution of the EMG may result in large decrements in SNR performance. Lastly, experimental data from constant-force, constant-angle, nonfatiguing contractions were examined. The experimentally observed densities fell in between the theoretic Gaussian and Laplacian densities. On average, the Gaussian density best fit the experimental data, although results varied with subject. For amplitude estimation, MAV processing had a slightly higher SNR than RMS processing. Index Terms—Biomedical signal processing, biological system modeling, electromyogram (EMG) amplitude estimation, elec-tromyography, modeling, myoelectric signal processing. I