STFT Phase Retrieval with Two Window Functions

Abstract

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.