Covariant time-frequency distributions based on conjugate operators

We propose classes of quadratic time-frequency distributions that retain the inner structure of Cohen's (see IEEE Trans. Signal Processing, vol.41, no.12, p.3275-3292, 1993) class. Each of these classes is based on a pair of "conjugate" unitary operators producing time-frequency displacements. The classes satisfy covariance and marginal properties corresponding to these operators. For each class, we define a "central member" generalizing the Wigner distribution and the Q-distribution, and we specify a transformation by which the class can be derived from Cohen's class.