The T-class of time–frequency distributions: Time-only kernels with amplitude estimation

Abstract

This paper presents a class of time–frequency distributions (TFDs) characterized by time-lag kernels which are functions of time only. If the parameters of the time-only kernels are properly chosen, their corresponding TFDs, the T-distributions, are more efficient than their two-dimensional counterparts in terms of cross-terms suppression while keeping a high-energy concentration (resolution) around the IF law of non-stationary signals. The proposed class is a subclass of Cohen's Class of quadratic TFDs. We have shown that separable time-lag kernels should be lag-independent (or time-only) for best resolution. In addition, non-parametric amplitude estimation is possible directly from the T-distributions in case of FM signals, a property that is not verified by other TFDs. Two examples of the T-distributions are given and their performance is compared to other TFDs with numerical examples using synthetic and real-life signals.