Design of IIR Filter using Remez Algorithm

Aashu Gupta,Dr Vijay Lamba,Er Munish Verma

doi:10.24297/ijct.v3i1b.2751

Abstract

In this paper, we present a numerical method for the equiripple approximation of Impulse Infinite Response digital filters. The proposed method is based on the formulation of a generalized eigenvalue problem by using Rational Remez Exchange algorithm. In this paper, conventional Remez algorithm is modified to get the ratio of weights in the different bands exactly. In Rational Remez, squared magnitude response of the IIR filter is approximated in the Chebyshev sense by solving for an eigenvalue problem, in which real maximum eigenvalue is chosen and corresponding to that eigenvectors are found, and from that optimal filter coefficients are obtained through few iterations with controlling the ratio of ripples.Â The design algorithm is computationally efficient because it not only retains the speed inherent in the Remez exchange algorithm but also simplifies the interpolation step.

Highlights

For designing FIR filters, the Remez algorithm is the wellknown method that guarantees optimality in the chebyshev sense
Though Remez algorithm is efficient algorithm but in its conventional low pass filter design, for example, when different weights are given for its pass-band and stop-band, one need to iteratively design the filter by trial and error to achieve the ratio of weights exactly
A modification in rational remez algorithm is made for the weights W (w) and ripples obtained depends on weight

Summary

Introduction

For designing FIR filters, the Remez algorithm is the wellknown method that guarantees optimality in the chebyshev sense. By transforming the elliptic filter to z-domain, an optimal filter that realizes equiripple both in pass-band and stop-band is obtained. Though Remez algorithm is efficient algorithm but in its conventional low pass filter design, for example, when different weights are given for its pass-band and stop-band, one need to iteratively design the filter by trial and error to achieve the ratio of weights exactly. This classical approach has critical limitations: 1.

Objectives

Methods

Conclusion