A necessary and sufficient condition for minimum phase and implications for phase retrieval

TL;DR

This paper establishes a practical necessary and sufficient condition for a function to be minimum phase, enabling unique phase retrieval from intensity measurements and analyzing related signal classes and transmission schemes.

Contribution

It provides a new, simpler criterion for minimum phase functions based solely on the function itself, not its complex analytic continuation.

Findings

Derived a necessary and sufficient condition for minimum phase functions.

Identified all band-limited signals with unique receiver states under intensity-only detection.

Discussed the performance of a linear detection transmission scheme.

Abstract

We give a necessary and sufficient condition for a function $E(t)$ being of minimum phase, and hence for its phase being univocally determined by its intensity $|E(t)|^2$. This condition is based on the knowledge of $E(t)$ alone and not of its analytic continuation in the complex plane, thus greatly simplifying its practical applicability. We apply these results to find the class of all band-limited signals that correspond to distinct receiver states when the detector is sensitive to the field intensity only and insensitive to the field phase, and discuss the performance of a recently proposed transmission scheme able to linearly detect all distinguishable states.