Time-varying filtering and signal estimation using Wigner distribution synthesis techniques

TLDR

The short‑time Fourier transform, ambiguity function, and Wigner distribution are mixed time‑frequency representations used to analyze local frequency characteristics, but synthesis techniques have not yet been developed for the Wigner distribution. The study aims to derive a signal synthesis algorithm that operates directly on the real‑valued high‑resolution Wigner distribution. The algorithm is implemented and illustrated through examples of time‑varying filtering and signal separation using the Wigner distribution.

Abstract

The short-time Fourier transform (STFT), the ambiguity function (AF), and the Wigner distribution (WD) are mixed time-frequency signal representations that use Fourier transform techniques to map a one-dimensional function of time into a two-dimensional function of time and frequency. These mixed time-frequency mappings have been used to analyze the local frequency characteristics of a variety of signals and systems. Although much work has also been done to develop STFT and AF synthesis algorithms that can be used to implement a variety of time-varying signal processing operations, no such synthesis techniques have thus far been developed for the WD. In this paper, a signal synthesis algorithm that works directly with the real-valued high-resolution WD will be derived. Examples of how this WD synthesis procedure can be used to perform time-varying filtering operations or signal separation will be given.