On the Injectivity of STFT Phase Retrieval with super-exponential decaying window function

TL;DR

This paper establishes conditions under which the phase retrieval problem from spectrograms is unique when using window functions with super-exponential decay, extending previous results for Gaussian windows.

Contribution

It provides new sufficient conditions for unique phase retrieval in the STFT setting with super-exponentially decaying windows, generalizing prior Gaussian window results.

Findings

Derived sufficient sampling conditions for unique phase retrieval.

Extended uniqueness guarantees beyond Gaussian windows.

Applicable to window functions with super-exponential decay.

Abstract

We investigate the uniqueness of short-time Fourier transform phase retrieval problems in $L^2(\mathbb{R})$. In particular, for underlying window functions whose Fourier transform decay faster than any exponential function, we derive sufficient conditions on discrete sampling sets for unique phase retrieval from the spectrogram. This result generalizes previous uniqueness guarantees on sampling sets for Gaussian windows.