Unifying distribution functions: some lesser known distributions

TL;DR

This paper presents a unified framework for various distribution functions used in signal analysis, including the Wigner, Cohen class, Husimi, and Glauber-Sudarshan distributions, highlighting their commonalities in representing signals in space and frequency.

Contribution

It introduces a unifying approach that consolidates multiple distribution functions into a single framework, enhancing understanding and potential applications.

Findings

Unified representation of multiple distribution functions

Connections between Wigner, Cohen, Husimi, and Glauber-Sudarshan functions

Potential for improved signal analysis techniques

Abstract

We show that there is a way to unify distribution functions that describe simultaneously a signal in space and (spatial) frequency. Probably the most known of them is the Wigner distribution function. Here we show how to unify functions of the Cohen class, Rihacek's complex energy function, Husimi and Glauber-Sudarshan distribution functions.