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 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 for real-valued signals.

我们考虑从短时傅立叶变换（STFT）测量的幅度进行相位检索的问题。众所周知，当下面的窗口具有无处不消失的模糊函数时，信号将由其STFT大小唯一确定（直到全局相位）。但是，当下面的窗口的模糊函数在某些时频平面上消失时，关于唯一相位可恢复性的说法还不清楚。在本文中，我们证明了通过考虑Paley-Wiener空间中的信号，可以证明STFT相位检索的新唯一性结果。其中，我们为实值信号的仅幅度样本建立了STFT相位检索的第一个唯一性定理。