We propose classes of quadratic time-frequency representations (QTFRs) that
are covariant to group delay shifts (GDSs). The GDS covariance QTFR proper
ty is important for analyzing signals propagating through dispersive system
s with frequency-dependent characteristics. This is because a QTFR satisfyi
ng this property provides a succinct representation whenever the time shift
is selected to match the frequency-dependent changes in the signal's group
delay that may occur in dispersive systems. We obtain the GDS covariant cl
asses from known QTFR classes (such as Cohen's class, the affine class, the
hyperbolic class, and the power classes) using warping transformations tha
t depend on the relevant group delay change. We provide the formulation of
the GDS covariant classes using two-dimensional (2-D) kernel functions, and
we list desirable QTFR properties and kernel constraints, as well as speci
fic class members. We present known examples of the GDS covariant classes,
and we provide a new class: the power exponential QTFR class. We study the
localized-kernel subclasses of the GDS covariant classes that simplify the
theoretical development as the kernels reduce from 2-D to one-dimensional (
I-D) functions, and we develop various intersections between the QTFR class
es. Finally, we present simulation results to demonstrate the advantage of
using T Rs that are matched to changes in the group delay of a signal.