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

• Published in: Compel 2014-01, Vol.33 (5), p.1831-1843
• Main Authors: Mirkovic, Dejan Dragan, Petkovic, Predrag M, Litovski, Vanco B
• Format: Article
• Language: English
• Subjects: Amplitudes; Approximation; Delay; Design; Differential equations; Digital filters; Distortion; Filter design (mathematics); Group delay; IIR filters; Laplace transforms; Mathematical analysis; Mathematical models; Methods; Numerical integration; Prototypes; Selectivity; Studies; Transfer functions; Transforms; Z transforms
• ISSN: 0332-1649; 2054-5606
• DOI: 10.1108/COMPEL-03-2014-0058

Purpose Development of a design 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.