A simple approximation algorithm to obtain sequences with nonnegative Fourier transforms

Author

Ramalingam, C.S. ; Vaccaro, R.J.

Author_Institution

Dept. of Electr. Eng., Rhode Island Univ., Kingston, RI, USA

Volume

39

Issue

6

fYear

1991

fDate

6/1/1991 12:00:00 AM

Firstpage

1459

Lastpage

1462

Abstract

A sequence {x[n]} is said to be positive if and only if its Fourier transform is nonnegative for all frequencies. A very simple computational algorithm is proposed 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

Keywords

fast Fourier transforms; least squares approximations; minimisation; series (mathematics); DFT; approximation algorithm; computational algorithm; discrete frequencies; least squares minimization; linear minimisation; nonnegative Fourier transforms; nonnegativity constraints; nonparametric sequences; parametric sequences; positive sequence; Adaptive signal processing; Approximation algorithms; Fourier transforms; Frequency; Least squares approximation; Least squares methods; Resonance light scattering; Signal processing algorithms; Speech processing; Sun;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.136560

Filename

136560