BILINEAR TIME-FREQUENCY REPRESENTATIONS - NEW INSIGHTS AND PROPERTIES

An analysis of the interference terms of Cohen-class bilinear time-frequency representations (TFR's) of multicomponent signals is presented. New insights are given, and new interference properties are defined for TFR's. Constraints for achieving these 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; i.e., it is not possible to simultaneously satisfy all of these properties in the class of bilinear TFR's. The useful class of product kernels are considered, and generalized further to allow TFR's with potentially superior interference properties. The interference frequency concentration and attenuation properties allow TFR's with spectrogram-like interference suppression, but without the spectrogram's inherent time/frequency resolution tradeoff. Other useful combininations of properties are discussed and analyzed. Properties and tradeoffs are illustrated via application of different TFR's to finite duration tones, linear FM sweeps, and speech. It is seen that those TFR's with the best interference frequency localization and attenuation properties yield the most lucid representations of the signals considered.