Errors in frequency parameters of EMG power spectra

The author derives approximate formulae for random error, expressed as a variance or a standard deviation, and random and systematic errors due to added noise valid for any spectrum of signal and noise. The findings are applied to two spectra, a rectangular spectrum, which allows analytical treatment, and a spectrum which resembles those seen in surface EMGs. Approximate expressions are derived for bias and standard deviation of the estimates for mean frequency, zero-crossing frequency, and fractile frequency. 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. 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 wideband white noise, the median frequency has the best immunity to noise.