Near-Linear-Phase IIR Filters Using Gauss-Newton Optimization

In this paper, we present a simple optimization-based method for designing near-linear-phase IIR filters based on the Gauss-Newton method, and we explore its benefits over symmetric FIR filters. We demonstrate IIR low-pass filters with lower group delay, lower order, and lower magnitude errors than corresponding FIR filters while still maintaining a phase response linearity of R2 ≥ 0.99 in the passband. Such filters can be beneficial in applications where approximate, rather than exact, linear phase is sufficient. Code is available on the author’s website.

[1]  Paul M. Chau,et al.  A technique for realizing linear phase IIR filters , 1991, IEEE Trans. Signal Process..

[2]  Thomas W. Parks,et al.  Design of IIR filters in the complex domain , 1990, IEEE Trans. Acoust. Speech Signal Process..

[3]  Guido M. Cortelazzo,et al.  Simultaneous design in both magnitude and group-delay of IIR and FIR filters based on multiple criterion optimization , 1984 .

[4]  A. W. Soewito,et al.  Least square digital filter design in the frequency domain , 1991 .

[5]  L. Mcbride,et al.  A technique for the identification of linear systems , 1965 .

[6]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[7]  Andreas Antoniou,et al.  Improved Design Method for Nearly Linear-Phase IIR Filters Using Constrained Optimization , 2013, IEEE Transactions on Signal Processing.

[8]  Thomas W. Parks,et al.  Design of FIR filters in the complex domain , 1987, IEEE Trans. Acoust. Speech Signal Process..

[9]  J. Kormylo,et al.  Two-pass recursive digital filter with zero phase shift , 1974 .

[10]  P. Lafrance,et al.  Digital filters , 1974, Proceedings of the IEEE.

[11]  Mathias C. Lang,et al.  Least-squares design of IIR filters with prescribed magnitude and phase responses and a pole radius constraint , 2000, IEEE Trans. Signal Process..

[12]  Arnab K. Shaw.  Optimal design of digital IIR filters by model-fitting frequency response data , 1993, ISCAS.