Biomedical signal processing (in four parts). Part 3. The power spectrum and coherence function

This is the third in a series of four tutorial papers on biomedical signal processing and concerns the estimation of the power spectrum (PS) and coherence function (CF) od biomedical data. The PS is introduced and its estimation by means of the discrete Fourier transform is considered in terms of the problem of resolution in the frequency domain. The periodogram is introduced and its variance, bias and the effects of windowing and smoothing are considered. The use of the autocovariance function as a stage in power spectral estimation is described and the effects of windows in the autocorrelation domain are compared with the related effects of windows in the original time domain. The concept of coherence is introduced and the many ways in which coherence functions might be estimated are considered.