Characterization of non-uniformly spaced discrete-time signals from their Fourier phase

Much work has been published on the characterization and reconstruction of signals from their Fourier phase and from nonuniformly spaced sample values. In certain applications, the only available measurements of a signal are nonuniformly spaced samples whose Fourier magnitude information is unavailable or known to be corrupted. This paper gives an alternate proof to Shitz´s and Zeevi´s (1985) theorem on unique characterization of nonuniformly spaced discrete-time signals from Fourier phase. They used Logan´s (1977) theorem on unique determination of a real, band-pass signal from its zero-crossings. This paper employs the more direct approach of representing signals as Weierstrass canonical products. This representation reveals the underlying structure of the signals and illuminates the effects of the hypotheses on them.