Time- Frequency Distributions Based on Conjugate Operators*

New classes of quadratic time-frequency representations (QTFRs), such as the affine, hyperbolic, and power classes, are interesting alternatives to the conventional shift-covariant class (Cohen's class). This paper studies new QTFR classes that retain the inner structure of Cohen's class. These classes are based on a pair of "conjugate" unitary operators and satisfy covariance and marginal properties. For each class, we define a "central member" generalizing the Wigner distribution, and we specify a transformation by which the class can be derived from Cohen's class.