Some results on the time-frequency sampling of the short-time Fourier transform magnitude

Nawab et al. [1] have shown that a signal can he reconstructed, under mild conditions, from knowledge of the magnitude of the short-time Fourier transform (STFT). The algorithm presented by Nawab for signal reconstruction requires knowledge of all of the STFT magnitude, regardless of window overlap. In this paper, we develop a general relationship between time and frequency sampling of the STFT magnitude. Specifically, we show that if an L point shift exists between adjacent windows in an STFT analysis, then almost any 2L samples of the STFT magnitude from each window are enough for signal reconstruction.