Properties and implementation of the exponential class of time-frequency representations

The exponential class (EC) quadratic time-frequency representations (QTFRs) are well-suited for analyzing signals passing through exponentially dispersive systems. We consider some important properties of EC QTFRs: a time-frequency concentration property along given group delay curves resulting in a localized-kernel subclass, and a time-shift covariance property resulting in the intersection of the EC with Cohen's (1966) class. We investigate several aspects of EC analysis important for practical applications. We study the time-frequency geometry of the exponential Wigner distribution, the central EC QTFR, and we investigate how to attenuate interference terms by means of smoothing. We also propose the implementation of EC QTFRs by warping affine class QTFRs, and we demonstrate the importance of the EC via simulation results.