Group Delay Equalization of Polynomial Recursive Digital Filters in Maximal Flat Sense

2019 ◽  
Vol 28 (10) ◽  
pp. 1950173 ◽  
Author(s):  
Negovan Stamenković ◽  
Nikola Stojanović ◽  
Goran Perinić
Keyword(s):  
Digital Filter ◽  
Digital Filters ◽  
Group Delay ◽  
Minimum Phase ◽  
Iir Filter ◽  
Delay Response ◽  
Cascade Connection ◽  
Allpass Filter ◽  
The Given ◽  
Recursive Digital Filters

The paper presents the development of an algorithm to obtain stable allpass filter, which acts as a group delay equalizer, with the aim to equalize group delay of the polynomial IIR filter in a maximal flat sense. The proposed method relies on a set of nonlinear equations, derived directly from the flatness conditions of the group delay response at the origin in the [Formula: see text]-plane, with the order to obtain the unknown values of the allpass filter coefficients. The algorithm implemented in the MATLAB platform returns the coefficients of allpass filter. In the given example, first we construct a minimum phase polynomial IIR digital filter with a maximally flat magnitude at origin, next we augment the system with cascade connection of nonminimum allpass digital filter with order to equalize the group delay response of the whole filter in a maximally flat sense.

A second order s-to-z transform and its implementation to IIR filter design

2014 ◽  
Vol 33 (5) ◽  
pp. 1831-1843 ◽  
Author(s):  
Dejan Mirković ◽  
Predrag Petković ◽  
Vančo Litovski
Keyword(s):  
Digital Filters ◽  
Group Delay ◽  
Transfer Functions ◽  
Filter Design ◽  
Second Order ◽  
Pass Band ◽  
Content Type ◽  
Iir Filter ◽  
Band Group ◽  
Iir Digital Filters

Purpose – The purpose of this paper is to design a tool for IIR digital filters obtained from analog prototypes, which preserves simultaneously the amplitude and the group delay response. Design/methodology/approach – A new s-to-z transform is developed based on a second order formula used for numerical integration of differential equations. Stability of the newly obtained transfer functions in the z-domain is proved to be preserved. Distortions introduced by the new transform into the original amplitude and group delay responses are studied. Findings – The new formula, when implemented to all-pole prototypes, exhibits lower selectivity than the original while reducing the pass-band group delay distortions. In the same time its structure is importantly simpler than the functions obtained by the well-known bilinear transform. When implemented to a prototype having “all kinds” of transmission zeros the resulting filter has almost ideally the same characteristic as the prototype. Research limitations/implications – The new transform may be used exclusively to synthesize even order filters. The new function is twice the order of the analog prototype. This kind of transformations are used to design IIR digital filters only. Low-pass transfer functions were studied being prototypes for all other cases. Originality/value – This is a new result never mentioned in the literature. Its effectiveness is confined to a niche problem when simultaneous sharp selectivity and low group delay distortions are sought.

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