Wigner-related phase spaces for signal processing and their optical implementation

Abstract

Phase spaces are different ways to represent signals. Owing to their properties, they are often used for signal compression and recognition with high discrimination abilities. We present several recently introduced Wigner-related sets of representations that have improved signal processing performance, and we introduce an optical implementation. This study deals with the generalized Wigner spaces, the fractional Fourier transform, and the x -p and the r -p representations. The optical implementations are demonstrated and discussed.

The Effect of Anisotropic Gaussian Schell-Model Sources in Generalized Phase Space Stokes Parameters

“…The Wigner distribution function depends in conjunction on the canonical conjugate phase space variables, which for light beams are the transverse position vector 𝐫 and the angular (spatial frequency) vector 𝐤, and for optical pulses are the time variable t and temporal frequency ω. The Wigner function which depends on both (𝐫, 𝐤, t, ω) can also be constructed [5]. We shall describe the Wigner phase space matrix by the integral of the shifted electric correlation matrix [2]…”

“…One of them is its use in imaging where one can obtain a simplified WDF of image wave field in a partially coherent microscope [3]. Another one is its utilization in signal processing where one can obtain amplitude and phase retrieval, signal recognition and such easily via Wigner distribution function [4,5]. Additional insight into the Wigner distribution can be one can achive wave field propagation through graded index media by means of Wigner distribution function [6].…”