Uniqueness of STFT phase retrieval for bandlimited functions

TL;DR

This paper investigates the conditions under which signals can be uniquely reconstructed from their STFT magnitude measurements, especially when the ambiguity function of the window function vanishes, and introduces new uniqueness results for bandlimited signals.

Contribution

It provides new theoretical guarantees for STFT phase retrieval in cases where the ambiguity function vanishes, including the first uniqueness theorem for real-valued bandlimited signals.

Findings

Unique phase retrieval for bandlimited signals in Paley-Wiener spaces.

First theorem establishing uniqueness from magnitude-only samples for real-valued signals.

Demonstrates conditions under which signals are uniquely determined up to global phase.

Abstract

We consider the problem of phase retrieval from magnitudes of short-time Fourier transform (STFT) measurements. It is well-known that signals are uniquely determined (up to global phase) by their STFT magnitude when the underlying window has an ambiguity function that is nowhere vanishing. It is less clear, however, what can be said in terms of unique phase-retrievability when the ambiguity function of the underlying window vanishes on some of the time-frequency plane. In this short note, we demonstrate that by considering signals in Paley-Wiener spaces, it is possible to prove new uniqueness results for STFT phase retrieval. Among those, we establish a first uniqueness theorem for STFT phase retrieval from magnitude-only samples in a real-valued setting.