Estimation of shape characteristics of surface muscle signal spectra from time domain data

Myoelectric manifestations of muscle fatigue have been described by monitoring the first-order moment (mean frequency) of the power spectral density function during voluntary or electrically elicited sustained contractions. Higher order central moments provide additional information about the width, skewness, and kurtosis of the spectrum and its shape changes, thereby providing a description of slow nonstationarities more accurate than that allowed by the mean frequency alone. In 1986, B. Saltzberg introduced a method of representing the moments of the power spectral density function of band limited signals, without computing the Fourier transform, as weighted sums of samples of the autocorrelation function. If one allows for oversampling of the signal (and therefore of its autocorrelation function), more efficient weighted sums can be found which give Saltzberg´s formula as a limiting case. The faster rate of decay of the weights implies a faster convergence of the estimates and the need to compute fewer samples of the autocorrelation function. The algorithm is particularly suitable for: 1) analysis of evoked potentials (M-waves), because it does not need zero padding to increase resolution and operates on any number of samples, and 2) on-line implementation by dedicated microprocessors performing simultaneous spectral moment analysis on a number of parallel channels.