STFT Phase Retrieval with Two Window Functions

TL;DR

This paper investigates the conditions under which signals can be uniquely reconstructed from the magnitude of their short-time Fourier transforms using two specific window functions, providing optimal sampling strategies and extending results to periodic and quasi-periodic signals.

Contribution

It establishes uniqueness results for STFT phase retrieval with two windows, identifies optimal sampling intervals, and extends the theory to periodic and quasi-periodic signals.

Findings

Unique determination of signals from two-window STFT magnitude samples.

Optimal sampling intervals for compactly supported windows.

Extension of results to periodic and quasi-periodic signals.

Abstract

In this paper, we consider the uniqueness of STFT phase retrieval with two window functions. We show that a complex-valued locally integrable nonseparable signal is uniquely determined up to a global phase by phaseless samples of its short time Fourier transforms with respect to two well-chosen window functions over countable parallel lines or certain lattices. Moreover, we give the optimal sampling interval for STFT phase retrieval with compactly supported window functions. For periodic locally integrable signals, we obtain a uniqueness result for STFT phase retrieval with sampled values over two parallel lines whose distance is an irrational multiple of the period. And for quasi-periodic signals, we obtain a similar result.