A Simple Approximation Algorithm to Obtain Sequences with Nonnegative Fourier Transforms

A sequence {x[n]} is said to be positive if and only if its Fourier transform is nonnegative for all frequencies. In this correspondence, we propose a very simple computational algorithm to obtain a positive sequence by minimally perturbing (in the least squares sense) a given nonpositive one. By imposing nonnegativity constraints at specific, discrete frequencies the least squares minimization becomes linear and, hence, easily solvable. This approach is shown to be applicable to nonparametric sequences, as well as to those with a parametric description. © 1991 IEE