Publications

Unique recovery of a signal from the magnitude (modulus) of the Fourier transform has been of long-standing interest in image and optical processing in which Fourier-transform phase is lost or difficult to measure. We investigate an alternative problem of recovering a signal from the Fourier-transform magnitude of overlapping regions of the signal, i.e., from the short-time (or -space) Fourier-transform magnitude. Recently it was established that a discrete-time signal x (n) can be uniquely obtained under mild restrictions from its short-time Fourier-transform magnitude. In this paper we extend this result to the case when the short-time Fourier-transform magnitude is known at only one or two frequencies for each n. We also present a recursive algorithm for recovering a sequence from such samples and demonstrate the algorithm with an example.

In this paper, a signal is shown to be uniquely represented by the magnitude of its short-time Fourier transform (STFT) under mild restrictions on the signal and the analysis window of the STFT. Furthermore, various algorithms are developed which reconstruct signal from appropriate samples of the STFT magnitude. Several of the algorithms can also be used to obtain signal estimates from the processed STFT magnitude, which generally does not have a valid short-time structure. These algorithms are successfully applied to the time-scale modification and noise reduction problems in speech processing. Finally, the results presented here have similar potential for other applications areas, including those with multidimensional signals.