The Cohen's class Since there is much more than one distribution satisfying properties (4.2), (4.3) and (4.4), we can impose additional constraints on $\rho_x$ so that this distribution satisfies other desirable properties. Among these, the covariance principles are of fundamental importance. The Cohen's class, to which is dedicated this section, and whose definition can be found in subsection 4.1.2, is the class of time-frequency energy distributions covariant by translations in time and in frequency [Coh89]. The spectrogram, that we considered in the previous part, is an element of the Cohen's class since it is quadratic, time- and frequency- covariant, and preserves energy (property (4.2)). However, taking the squared modulus of an atomic decomposition is only a restrictive possibility to define a quadratic representation, and this definition presents the drawback that the marginal properties (4.3) and (4.4) are not satisfied.
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