All-Pole Recursive Digital Filters Design Based on Ultraspherical Polynomials
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A simple method for approximation of all-pole recursive digital filters, directly in digital domain, is described. Transfer function of these filters, referred to as Ultraspherical filters, is controlled by order of the Ultraspherical polynomial, nu. Parameter nu, restricted to be a nonnegative real number (nu ≥ 0), controls ripple peaks in the passband of the magnitude response and enables a trade-off between the passband loss and the group delay response of the resulting filter. Chebyshev filters of the first and of the second kind, and also Legendre and Butterworth filters are shown to be special cases of these allpole recursive digital filters. Closed form equations for the computation of the filter coefficients are provided. The design technique is illustrated with examples.
KeywordsAll-pole IIR filter, lowpass filtes, highpass filters, ultraspherical filter, approximation theory
Document typePeer reviewed
Document versionFinal PDF
SourceRadioengineering. 2014, vol. 23, č. 3, s. 949-953. ISSN 1210-2512
- 2014/3