STFT Phase Retrieval with Two Window Functions

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.

💡 Research Summary

This paper investigates the uniqueness of short‑time Fourier transform (STFT) phase retrieval when two specially designed window functions are employed. The authors focus on complex‑valued, locally integrable signals that are “non‑separable” in the sense that they do not vanish on any interval of a prescribed length. The main contributions can be summarized as follows.

1. Two‑window framework. Let ϕ be a compactly supported, real‑valued window with support in