Abstract
We present a review of the applications of the Wigner distribution function in various areas of signal processing: amplitude and phase retrieval, signal recognition, characterization of arbitrary signals, optical systems and devices, and coupling coefficient estimation in phase space. Although reference is made to specific signals and systems, the mathematical formulation is general and can be applied to either spatial, temporal, or spatio-temporal phase spaces, to coherent, partially coherent, or discrete signals. The universal and intuitive character of the Wigner distribution approach to signal characterization and processing and its simplicity in solving many issues are evidenced throughout the paper.
Highlights
Phase space methods become increasingly exploited in signal processing applications due to their intuitive character, universal validity, and last but not least simplicity in an increasing number of practical situations
There are many phase space distribution functions that can be employed in signal processing applications; the spectrogram, the ambiguity function, or the Wigner distribution function (WDF) are just a few examples
This paper focuses on the applications of the WDF in signal processing; this phase space distribution function is often referred to as Wigner-Ville distribution, but the WDF term is used in a larger range of applications and the term WDF will be used throughout this paper
Summary
Phase space methods become increasingly exploited in signal processing applications due to their intuitive character, universal validity, and last but not least simplicity in an increasing number of practical situations. These methods refer to any description of a signal or an optical system through a function that depends jointly on the canonical conjugate phase space variables, which are the transverse position vector r and the angular (spatial frequency) vector k for light beams, the time variable t, and frequency ω for optical pulses or, more generally, all four coordinates r, k, t, and ω. The responsibility of doing justice to the so many briefly mentioned issues is entrusted to the references
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