Bilinear time-frequency representations: new insights and properties

An analysis of the interference terms of Cohen-class bilinear time-frequency representations (TFR) of multicomponent signals is presented. Constraints for achieving new interference properties are derived. Imposing these interference time and interference frequency concentration constraints on a TFR guarantees that the TFR will be zero everywhere the signal s(t) is zero, and the TFR will contain only those frequencies that occur in the signal. Thus, these new constraints guarantee strong finite support in a TFR. When these interference concentration properties are combined with interference attenuation, tradeoffs between finite support, the marginals, and the interference properties are shown to be unavoidable. The useful class of product kernels are considered and generalized further to allow TFR with potentially superior interference properties. The interference frequency concentration and attenuation properties allow TFR with spectrogram-like interference suppression, but without the spectrogram´s inherent time/frequency resolution tradeoff. Other useful combinations of properties are discussed and analyzed, and properties and tradeoffs are illustrated by examples