5. Time-frequency analysis of non-stationary signals

Time-frequency representation is dedicated to non-stationary signals and can be considered as an extension of classical Fourier analysis. The non-stationarity of signals corresponds, for example, to sudden jumps or variations in frequency characteristics over time: most of the information is carried by non-stationarity. Hence the need for time-dependent spectral analysis.

A representation of the signal as a function of time alone gives little indication of its frequency behavior, while its Fourier analysis masks the instant of emission and the duration of each of the signal's events, since the Fourier transform gives information that eliminates time dependency by providing frequency information "averaged" over the entire duration of the signal.

This idea of joint representation in time and frequency is reminiscent of reading a musical score,...