Abstract

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.

© 1983 Optical Society of America

Stability of unique Fourier-transform phase reconstruction

Jorge L. C. Sanz, Thomas S. Huang, and Fernando Cukierman
J. Opt. Soc. Am. 73(11) 1442-1445 (1983)

Unique reconstruction of a band-limited multidimensional signal from its phase or magnitude

Jorge L. C. Sanz and Thomas S. Huang
J. Opt. Soc. Am. 73(11) 1446-1450 (1983)

Signal synthesis and reconstruction from partial Fourier-domain information

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