Abstract
In the present paper, we discuss a method to design a linear phase 1-dimensional Infinite Impulse Response (IIR) filter using orthogonal polynomials. The filter is designed using a set of object functions. These object functions are realized using a set of orthogonal polynomials. The method includes placement of zeros and poles in such a way that the amplitude characteristics are not changed while we change the phase characteristics of the resulting IIR filter.
Highlights
In the past two to two and half decades, a great deal of work has been carried out in the field of design of linear phase Infinite Impulse Response (IIR) filters
IIR filters are designed with equiripple or maximally flat group delay [3]
It is not possible to calculate f (x) using infinite number of orthogonal polynomial terms; we find the approximate object function fa(x) using only first (N + 1) polynomial terms fa(x) = a2nP2n(x)
Summary
In the past two to two and half decades, a great deal of work has been carried out in the field of design of linear phase IIR filters. IIR filters are designed with equiripple or maximally flat group delay [3] To directly design a linear phase IIR filter, Lu et al [7] give an iterative procedure, it is based on a weighted least-squares algorithm. Xiao et al [8] discusse a method to design a linear phase IIR filter with frequency weighted least-square error optimization using Broyden-Fletcher-Goldfarb-Shanno (BFGS) [9] method. A procedure to design linear phase IIR filter from linear phase FIR filter has been discussed by Holford et al [12] using frequency weighting model reduction for highly selective filters. The present paper discusses a technique to design IIR filters with approximately linear phase.
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