Uniqueness of STFT phase retrieval for bandlimited functions

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