Time-frequency Representation Of Signal Research Articles

Signal synthesis from pseudo-Wigner distribution and applications

This paper is concerned with mixed time-frequency signal representation and processing using pseudo-Wigner distribution (PWD). In this approach, the PWD is modified, and a signal is to be synthesized from the modified PWD. Two algorithms, the "outer-product approximation" (OPA) and the "overlapping method" (OM), based on outer-product formulation are presented. Experimental results include noise smoothing and signal separation in the time-frequency domain.

An acoustooptic Wigner processor for time-varying signal analysis

The Wigner distribution, or WD, produces a time-frequency signal representation from which the time- and/or frequency-domain properties of a signal can be extracted. To operate at very high data rates, an acoustooptic specialized Wigner distribution processor is proposed.

EURASIP short course on “time-frequency representation of signals and related applications”: February 18–20, 1987, Lyon, France

EURASIP short course on “time-frequency representation of signals and related applications”: February 18–20, 1987, Lyon, France

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.

The aliasing problem in discrete-time Wigner distributions

There is no straightforward way to proceed from the continuous-time Wigner distribution to a discrete-time version of this time-frequency signal representation. A previously given definition of such a function turned out to yield a distribution that was periodic with period π instead of 2π and this caused aliasing to occur. Various alternative definitions are considered and compared with respect to aliasing and computational complexity. From this comparison it appears that no definition leads to a function that is optimum in all respects. This is illustrated by an example.

The time-dependent physical spectrum of light and the wigner distribution function

A connection is made between the Wigner distribution function and the time-dependent physical spectrum of light. The physical spectrum is a measurable quantity characterizing nonstationary light sources whereas the Wigner distribution function is a more abstract time-frequency representation of signals. The connection between both quantities is useful because it provides insight in the meaning of time-dependent spectra and it gives an intuitive understanding of the uncertainty of simultaneous time-frequency measurements.