Errors in frequency parameters of EMG power spectra

Frequency shifts in random signals, e.g., EMG or Doppler ultrasound, can be followed by monitoring one or more parameters of the power spectrum. When such a frequency parameter is determined over a finite length of the signal, a random error and sometimes a systematic error or bias are introduced. Approximate expressions, in terms of moments of the power spectrum, have been derived for bias and standard deviation of the estimates for mean frequency, zero-crossing frequency, and fractile frequency (of which the median frequency is a special case). Experimental results from surface EMG recordings of three human muscles in constant force isometric contractions were in agreement with the theoretical predictions. In this case the mean frequency had the smallest random error. It turned out that the measured values of the zero-crossing frequency can deviate considerably from the predictions by the Rice formula when the amplitude distribution is not exactly Gaussian. In the presence of noise, all frequency parameters show a systematic deviation, depending on the signal-to-noise ratio. In addition to known results on this deviation for mean and zero-crossing frequency, an exact and an approximate expression for the fractile frequency are given. In the case of EMG plus wide-band white noise, the median frequency has the best immunity to noise.