An Improved Design of High-Resolution Quadratic Time–Frequency Distributions for the Analysis of Nonstationary Multicomponent Signals Using Directional Compact Kernels

Abstract

This paper presents a new advanced methodology for designing high resolution time–frequency distributions (TFDs) of multicomponent nonstationary signals that can be approximated using piece-wise linear frequency modulated (PW-LFM) signals. Most previous kernel design methods assumed that signals auto-terms are mostly centered around the origin of the $(\nu,\tau)$ ambiguity domain while signal cross-terms are mostly away from the origin. This study uses a multicomponent test signal for which each component is modeled as a PW-LFM signal; it finds that the above assumption is a very rough approximation of the location of the auto-terms energy and cross-terms energy in the ambiguity domain and it is only valid for signals that are well separated in the $(t,f)$ domain. A refined investigation led to improved specifications for separating cross-terms from auto-terms in the $(\nu,\tau)$ ambiguity domain. The resulting approach first represents the signal in the ambiguity domain, and then applies a multidirectional signal dependent compact kernel that accounts for the direction of the auto-terms energy. The resulting multidirectional distribution (MDD) approach proves to be more effective than classical methods like extended modified B distribution, S-method, or compact kernel distribution in terms of auto-terms resolution and cross-terms suppression. Results on simulated and real data validate the improved performance of the MDD, showing up to 8% gain as compared to more standard state-of-the-art TFDs.