Conclusion The Cohen's class, which gather all the quadratic time-frequency distributions covariant by shifts in time and in frequency, offers a wide set of powerful tools to analyze non-stationary signals. The basic idea is to devise a joint function of time and frequency that describes the energy density or intensity of a signal simultaneously in time and in frequency. The most important element of this class is probably the Wigner-Ville distribution, which satisfies many desirable properties. Since these distributions are quadratic, they introduce cross-terms in the time-frequency plane which can disturb the readability of the representation. One way to attenuate these interferences is to smooth the distribution in time and in frequency, according to their structure. But the consequence of this is a decrease of the time and frequency resolutions, and more generally a loss of theoretical properties. The general formulation proposed by Cohen is very useful to have a better understanding of the existing solutions, as well as the connection with the ambiguity function. But there exists other time-frequency energy distributions, which are not elements of the Cohen's class, i.e. which are not covariant by shifts in time or in frequency. This is the case for example of the affine distributions, which are presented in the next chapter.
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