Complex chebyshev approximation for IIR digital filters with arbitrary log magnitude and phase functions

Abstract

AbstractThis paper proposes a technique for designing IIR digital filters to have prescribed magnitude and phase responses. The technique is based on an iterative weighted least‐squares approach in the frequency domain.A weight updating procedure is introduced to minimize the complex logarithmic error in the Chebyshev sense. The real and imaginary parts of the complex logarithmic error represents the log magnitude and phase errors, respectively. Both the log magnitude and phase errors of the resulting filter become nearly equiripple. Filter coefficients at each iteration are computed efficiently using FFT and a fast recursive algorithm for a set of linear equations derived from the weighted least‐squares problem. Several design examples are shown to demonstrate the effectiveness of the proposed technique.