Localized subclasses of quadratic time-frequency representations

We discuss the existence of classes of quadratic time-frequency representations (QTFRs), e.g. Cohen, power, and generalized time-shift covariant, that satisfy a time-frequency (TF) concentration property. This important property yields perfect QTFR concentration along group delay curves. It also (1) simplifies the QTFR formulation and property kernel constraints as the kernel reduces from 2-D to 1-D, (2) reduces the QTFR computational complexity, and (3) yields simplified design algorithms. We derive the intersection of Cohen´s class with the new power exponential class, and show that it belongs to Cohen´s localized-kernel subclass. In addition to the TF shift covariance and concentration properties, these intersection QTFRs preserve power exponential time shifts, important for analyzing signals passing through exponentially dispersive systems