This paper presents a neural network (NN) approach for constructing timedomain signals from phases of their discrete Fourier transforms, to solve the socalled magnitude retrieval problem. The solution of the magnitude retrieval problem is not unique in general. In this paper, we impose two constraints (nonnegativity and not having conjugate reciprocal ztransform zeros) to obtain a unique solution by a neural network. The neural network structure we propose is a multilayer perceptron (MLP) with sigmoid function and backpropagation learning rule. Using simulation studies, we illustrate the capability of this NN structure in solving the magnitude retrieval problem for discrete signals. The NN approach presented in this paper is fast, always generates a specific solution, i.e., the nonnegative solution, and is not sensitive to the observation noise. A combination of the NN approach and a classical approach (alternating projections) can eliminate the deficiencies of both methods.
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