On the design of IIR digital filter using linearized equation systems

Abstract

This paper introduces a novel procedure for the design of IIR digital filters using linearized equation systems. The equations are related to the poles and zeros radii and angles, and are obtained via Taylor Series Expansion. The premise is that the IIR filters satisfy a given set of magnitude response specifications, achieving maximum deviation at determined number of extreme points, related to the number of poles and zeros. The proposed procedure makes it easier the addition of constraints such as maximally flatness, fixed transmission zeros, phase distortion, and most importantly, guarantees filter stability. Efficiency of the technique, robustness and phase distortion are shown through computer simulation results.

Holistic Biquadratic IIR Filter Design for Communication Systems Using Differential Evolution

“…Especially for IIR filters designed to meet certain filter specifications such as pass-band ripple, cutoff frequency, stop-band frequency, or stop-band attenuation, it is common to adjust poles and zeros in the -plane as this automatically ensures stability [27]. However, for a digital implementation, coefficients still need to be calculated out of the poles/zeros and quantised.…”

“…Furthermore, depending on the filter structure, scaling factors that are used to limit the numerical range for finite-wordlength architectures do not come out from such designs in the -plane. That is why, in contrast to [27], we adjust the coefficients of the filter directly in order to avoid this issue. To verify stability of these coefficients, poles and zeros need to be computed.…”