FIR filter optimization with POS3POLY in CVX

Author

Sicleru, Bogdan C. ; Dumitrescu, Bogdan

Author_Institution

Dept. of Autom. Control & Comput., Politeh. Univ. of Bucharest, Bucharest, Romania

fYear

2011

fDate

Aug. 29 2011-Sept. 2 2011

Firstpage

1405

Lastpage

1409

Abstract

POS3POLY is a new library for solving convex optimization problems with positive polynomials, designed and written by the current authors. POS3POLY allows simple descriptions of three types of positive multivariate polynomials, namely trigonometric, real and hybrid, sparing the user of the task of parameterizing them with linear matrix inequalities. Positivity on semialgebraic domains and a polynomial Bounded Real Lemma are also treated. In this paper, we present the features of POS3POLY that allow the manipulation of positive trigonometric polynomials in CVX and are useful in FIR filter optimization. Three fully detailed examples are given, for designing peak-constrained least-squares linear-phase filters, sparse 2D linear-phase filters and 2D approximately linear-phase filters.

Keywords

FIR filters; convex programming; least squares approximations; linear matrix inequalities; linear phase filters; polynomial matrices; signal denoising; sparse matrices; 2D approximately linear phase filters; CVX; FIR filter optimization; POS3POLY features; convex optimization problem; hybrid polynomials; linear matrix inequalities; parameterizing task; peak-constrained least squares linear phase filter; polynomial bounded real lemma; positive multivariate polynomials; real polynomials; semialgebraic domains; sparse 2D linear phase filter; trigonometric polynomials; Convex functions; Finite impulse response filters; Optimization; Passband; Polynomials; Programming; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Signal Processing Conference, 2011 19th European

Conference_Location

Barcelona

ISSN

2076-1465

Type

conf

Filename

7073862