Displacement-covariant time-frequency energy distributions

Important classes of quadratic time-frequency representations (QTFRs), such as Cohen´s (1966) class and the affine, hyperbolic, and power classes, are special cases within a general theory of displacement-covariant QTFRs. We present a theory of quadratic time-frequency energy distributions that satisfy a covariance property and generalized marginal properties. The theory coincides with the characteristic function method of Cohen and Baraniuk (see Proc. ICASSP-94, vol.3, p.357-360, 1994) in the special case of “conjugate operators”