Non stationary signals This chapter presents some useful definitions that constitute the background of time-frequency analysis (most of the information presented in this tutorial are extracted from [Fla93]). After a brief recall on time-domain and frequency-domain representations, we introduce the concepts of time and frequency localizations, time-bandwidth product and the constraint associated to this product (the Heisenberg-Gabor inequality). Then, the instantaneous frequency and the group delay are presented as a first solution to the problem of time localization of the spectrum. We carry on by defining non-stationarity from its opposite, stationarity, and show how to synthesize such non-stationary signals with the toolbox. Finally, we show that in the case of multi-component signals, these mono-dimensional functions (instantaneous frequency and group delay) are not sufficient to represent these signals ; a two-dimensional description (function of time and frequency) is necessary.
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