On the design of L/sub p/ IIR filters with arbitrary frequency response

This paper introduces an iterative algorithm for designing IIR digital filters that minimize a complex approximation error in an L/sub p/ sense. The algorithm combines ideas that have proven successful in the similar problem of L/sub p/ FIR filter design. We use iterative prefiltering techniques common in applications such as parameter estimation together with an iterative reweighted least squares (IRLS) method. The result is a double iterative approach that generates IIR filters of arbitrary magnitude and phase response and arbitrary numerator and denominator orders. Such filters can be used in a variety of applications in which the typical L/sub 2/ or L/sub /spl infin// error criteria might not be suitable.

[1]  S. Treitel,et al.  Fast l p solution of large, sparse, linear systems: application to seismic travel time tomography , 1988 .

[2]  Monson H. Hayes,et al.  Statistical Digital Signal Processing and Modeling , 1996 .

[3]  Keh-Shew Lu,et al.  DIGITAL FILTER DESIGN , 1973 .

[4]  C. S. Burrus,et al.  Least p-power error design of FIR filters , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[5]  E. C. Levy.  Complex-curve fitting , 1959, IRE Transactions on Automatic Control.

[6]  C. Sidney Burrus,et al.  Iterative reweighted least-squares design of FIR filters , 1994, IEEE Trans. Signal Process..

[7]  L. Goddard.  Approximation of Functions , 1965, Nature.

[8]  C. Sanathanan,et al.  Transfer function synthesis as a ratio of two complex polynomials , 1963 .

[9]  P. Laguna,et al.  Signal Processing , 2002, Yearbook of Medical Informatics.

[10]  Kenneth Steiglitz,et al.  Time-Domain Approximation by Iterative Methods , 1966 .

[11]  Stephen A. Dyer,et al.  Digital signal processing , 2018, 8th International Multitopic Conference, 2004. Proceedings of INMIC 2004..

[12]  R. Wolke,et al.  Iteratively Reweighted Least Squares: Algorithms, Convergence Analysis, and Numerical Comparisons , 1988 .

[13]  K. Steiglitz.  Computer-aided design of recursive digital filters , 1970 .

[14]  C. Sidney Burrus,et al.  Adaptive iterative reweighted least squares design of L/sub p/ FIR filters , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

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