Time-Frequency Distributions Based on Compact Support Kernels: Properties and Performance Evaluation

Abstract

This paper presents two new time-frequency distributions (TFDs) based on kernels with compact support (KCS) namely the separable (CB) (SCB) and the polynomial CB (PCB) TFDs. The implementation of this family of TFDs follows the method developed for the Cheriet-Belouchrani (CB) TFD. The mathematical properties of these three TFDs are analyzed and their performance is compared to the best classical quadratic TFDs using several tests on multi-component signals with linear and nonlinear frequency modulation (FM) components including the noise effects. Instead of relying solely on visual inspection of the time-frequency domain plots, comparisons include the time slices’ plots and the evaluation of the Boashash-Sucic’s normalized instantaneous resolution performance measure that permits to provide the optimized TFD using a specific methodology. In all presented examples, the KCS-TFDs show a significant interference rejection, with the component energy concentration around their respective instantaneous frequency laws yielding high resolution measure values.