Generalized time-shift covariant quadratic time-frequency representations with arbitrary group delays

We propose new classes of quadratic time-frequency representations (QTFRs) that satisfy the generalized time-shift covariance property important for analyzing signals propagating through systems with group delay dependent characteristics. We obtain these classes from Cohen´s (1966) class and the affine class of constant time-shift covariant QTFRs using a generalized warping that depends on the desirable group delay time-shift covariance. We develop formulations for the new classes, desirable properties with kernel constraints, new QTFR members, and intersection subclasses. We also propose the new exponential class of frequency-shift covariant and exponential time-shift covariant QTFRs.