Time–Frequency Analysis
John L. Semmlow, Benjamin Griffel · 2021
The spectral analysis techniques developed so far represent powerful signal-processing tools but are not very useful if the people are interested in the timing of particular events in the signal. Classical and modern spectral methods also assume that waveforms are stationary, that is, the waveforms do not change their basic properties (their statistical properties) over the analysis period. The Wigner–Ville distribution and others of Cohen’s class use an approach that harkens back to the early use of the autocorrelation function for calculating the power spectrum. All the transformations in Cohen’s class of distributions produce better results when applied to a modified version of the signal termed the analytic signal. The existence of cross-products in the Wigner–Ville transformation has motived the development of other distributions. Signals that show interesting variations in their properties over time are common in biology and medicine. This chapter presented two different approaches to defining the spectral changes with time.