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

When the surface electromyogram (EMG) generated from constant-force, consta nt-angle, nonfatiguing contractions is modeled as a random process, its den sity is typically assumed to be Gaussian. This assumption leads to root-mea n-square (RMS) processing as the maximum likelihood estimator of the EMG am plitude (where EMG amplitude is defined as the standard deviation of the ra ndom process). Contrary to this theoretical formulation, experimental work has found the signal-to-noise-ratio [(SNR), defined as the mean of the ampl itude 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 perfor mance 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 th at the MAV processor is the maximum likelihood estimator of the EMG amplitu de for the Laplacian model. SNR performance based on a Laplacian model is p redicted to be inferior to that of the Gaussian model by approximately 32%. Thus, minor variations in the probability distribution of the EMG may resu lt in large decrements in SNR performance. Lastly, experimental data from c onstant-force, constant-angle, nonfatiguing contractions were examined. The experimentally observed densities fell in between the theoretic Gaussian a nd Laplacian densities, On average, the Gaussian density best fit the exper imental data, although results varied with subject. For amplitude estimatio n, MAV processing had a slightly higher SNR than RMS processing.