Design of Linear Phase IIR Filters with Flat Magnitude Response using Complex Coefficients Allpole Filters

Diseño de Filtros IIR de Fase Lineal con Respuesta en Magnitud Plana usando Filtros Todopolo con Coeficientes Complejos

Alfonso Fernandez Vazquez¹ and Gordana Jovanovic Dolecek²

¹ School of Electronic Engineering; Xidian University No.2 South TaiBai Road; Xian, Shaanxi 710071; P. R. China afernan@inaoep.mx

² Department of Electronics; Instituto Nacional de Astrofisica, Optica, y Electronica, INAOE Luis Enrique Erro No. 1; Tonantzintla, Puebla 72840; Puebla, Mexico gordana@inaoep.mx

Article received on March 15, 2007
Accepted on September 03, 2007

Abstract

This paper presents a new method for the design of linear phase IIR filters with flat magnitude response. The method is based on the design of flat digital allpole filters with complex coefficients. Depending on the parity of the allpole filter order the resulting IIR filter have either real or complex coefficients. The parameters of the design are the same as in traditional IIR filter design, i.e., passband and stopband frequencies, ω_p and ω_s, passband droop A_p , and stopband attenuation A_s . Several design examples are provided to illustrate the method. In addition, a design of linear phase modified two–band IIR filter banks and a design of stable IIR filter with an improved group delay are presented as two applications of the proposed method.

Keywords: IIR filters, linear phase, allpole filters, allpass filters, filter banks, improved group delay.

Resumen

Este artículo presenta un nuevo método para el diseño de filtros IIR de fase lineal con respuesta en magnitud plana. El método esta basado en el diseño de filtros todopolo con respuesta plana y coeficientes complejos. Dependiendo de la paridad del orden del filtro todopolo, los filtros resultantes IIR tienen coeficientes reales o complejos. Los parámetros de diseño son los mimos que en el diseño tradicional de filtros IIR, esto es, frecuencias de paso y rechazo, ω_p y ω_s, y atenuaciones en la banda de paso y rechazo, A_p y A_s. Varios ejemplos de diseño son dados para ilustrar el método. Finalmente, el diseño de bancos de filtros modificado de dos bandas de fase lineal y el diseño de filtros IIR con retardo de grupo mejorado se presentan como dos aplicaciones del método propuesto.

Palabras clave: Filtros IIR, fase lineal, filtros todopolo, filtros pasatodo, banco de filtros, retardo de grupo mejorado.

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Acknowledgments

This work was supported by CONACyT Mexico under project number 49640.

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