Uniqueness of STFT phase retrieval for bandlimited functions

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.

arXiv comment13 pages, 5 figures

References in corpus (4)

• Sparse Phase Retrieval from Short-Time Fourier Measurements
• Reconstruction of Bandlimited Functions from Unsigned Samples
• A Non-iterative Method for (Re)Construction of Phase from STFT Magnitude
• Estimation of Overspread Scattering Functions

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• Phase retrieval of entire functions and its implications for Gabor phase retrieval
• On the connection between uniqueness from samples and stability in Gabor phase retrieval
• Phase Retrieval for $L^2([-\pi ,\pi ])$ via the Provably Accurate and Noise Robust Numerical Inversion of Spectrogram Measurements