Construction of fourth-order Cohen´s class: A deductive approach

A deductive construction of the fourth-order Cohen´s class is presented. It contains all the fourth-order time-frequency distributions which are time- and frequency-shift invariant. After introducing the related stationary trispectrum for complex signals, the authors present the general form that a fourth-order time-frequency representations must have in order to be time- and frequency-shift invariant. They examine some properties of the members of the fourth-order Cohen´s class and exhibit two of these members: the 4-Wigner-Ville distribution and the trispectrogram. It is shown that a desired property of a distribution is equivalent to a constraint on the kernel which parametrized the representation. Simple examples are given