Enhancement of a compact support time-frequency distribution derived from a polynomial kernel using image processing

The polynomial Cheriet-Belouchrani distribution (PCBD) is considered to be one of the best time-frequency distributins (TFDs) available for the analysis of time varying signals. As for all quadratic distributions, due to the unavoidable smoothing effects of the kernel, the recently proposed PCBD suffers from degradation of time-frequency localization. The aim of this paper is to enhance the readability and improve the concentration of this distribution. The obtained time-frequency map is enhanced using a specific method based on two-dimensional mean filter, automatic binarization and morphological image processing techniques. The enhanced PCBD is compared to the original distribution using several tests on real-life and multi-component signals with linear and nonlinear frequency modulation (FM) components including the noise effects. Also, comparisons are made by considering a selection of the best-known time-frequency representations (TFRs).