The exponential class and generalized time-shift covariant quadratic time-frequency representations

We propose the new exponential class of quadratic time-frequency representations (QTFRs) covariant to constant shifts in frequency and dispersive, exponential shifts in time. We obtain the exponential class from the two covariance properties it satisfies, and also by warping the affine class of scale and constant time-shift covariant QTFRs. We develop the class formulation, kernel constraints for desirable properties, new QTFR members, and the intersection of the exponential class with Cohen's class. We also propose QTFR classes that are covariant to generalized time-shifts according to arbitrary group delay functions. We obtain these classes from known QTFR classes (such as Cohen's class, the affine class, the hyperbolic class, and the power classes) using a generalized transformation based on the desirable group delay time-shift covariance.