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

Hayes (1980) presented conditions under which a sequence of real numbers is uniquely specified to within a sign factor and an integral, horizontal translation by the magnitude of its Fourier transform. This paper presents conditions under which a complex-valued, discrete-time function of finite duration is uniquely determined to within a time shift and a multiplicative constant of unit modulus by its Fourier magnitude. The result presented here is a generalization of Hayes' result. The proof of the theorem utilizes Hadamard's factorization theorem and is different from previous approaches.