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

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.