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The Design of Sparse and Non-sparse FIR Filters Using Linear Complementarity Problem Approach

Authors:
Muhammad Muzammal Naseer
Kamal Harb
Ahmad Nuseirat

Keywords: Finite Impulse Response; Lemke’s algorithm; Linear Comlimentarity Problem; Quadratic Program

Abstract:
In this article, the problem of linear phase finite impulse response (FIR) filter design is reconsidered as a linear complementarity problem (LCP) with a weighting strategy. The LCP is not an optimization technique because there is no objective function to optimize; however, quadratic programming, one of the applications of LCP, can be used to find an optimal solution for the 1D FIR filter. Quadratic programs are an extremely important source of applications of LCP; in fact, several algorithms for quadratic programs are based on LCP. It has been shown that, by selecting proper weights, the LCP approach is capable of producing equiripple response. Since length of the impulse response of discrete time filters is often an indicator of computational cost, an algorithm is proposed that iteratively thins the impulse response of a non-sparse filter. The resulting LCP has been solved by a computationally effective Lemke’s algorithm. Different examples are presented to illustrate the efficiency of the proposed methods.

Pages: 7 to 11

Copyright: Copyright (c) IARIA, 2016

Publication date: February 21, 2016

Published in: conference

ISSN: 2308-4480

ISBN: 978-1-61208-453-4

Location: Lisbon, Portugal

Dates: from February 21, 2016 to February 25, 2016