Optimum lowpass and bandpass filter approximation

Beccari, C.; Molinaro, M.

doi:10.1002/cta.4490090403

Cited by 1 publication

(1 citation statement)

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“…Some methods for introducing optimisation of the transfer properties in the approximation problem of amplitude, phase and delay are recommended in Rakovich (1974Rakovich ( , 1977, Beccari (1977Beccari ( , 1979, Rakovich and Popovich (1978) and Beccari and Molinaro (1981).…”

Section: Introductionmentioning

confidence: 99%

New class of filter functions generated most directly by Christoffel-Darboux formula for Gegenbauer orthogonal polynomials

Ilić

Pavlović

2011

International Journal of Electronics

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A new original formulation of all pole low-pass filter functions is proposed in this article. The starting point in solving the approximation problem is a direct application of the Christoffel-Darboux formula for the set of orthogonal polynomials, including Gegenbauer orthogonal polynomials in the finite interval [71, þ1] with the application of a weighting function with a single free parameter. A general solution for the filter functions is obtained in a compact explicit form, which is shown to enable generation of the Gegenbauer filter functions in a simple way by choosing the value of the free parameter. Moreover, the proposed solution with the same criterion of approximation could be used to generate Legendre and Chebyshev filter functions of the first and second kind as well. The examples of proposed filter functions of even (10th) and odd (11th) order are illustrated. The approximation is shown to yield a good compromise solution with respect to the filter frequency characteristics (magnitude as well as phase characteristics). The influence of tolerance of the filter critical component (inductor) on the proposed magnitude and group delay characteristics of a resistively terminated LC lossless ladder filter is analysed as well. The proposed filter functions are superior in terms of the excellent magnitude characteristic, which approximates an ideal filter almost perfectly over the entire pass-band range and exhibits the summed sensitivity function better than that of a Butterworth filter. In the article, we present the filter function solution that exhibits optimum amplitude as well as optimum group delay characteristics that are of crucial importance for implementation of digital processing as well as RF analogue parts of communication networks. Derivation of the other band range filter functions, which could be realised either by continuous or digital filters, is also generally possible with the procedure proposed in this article.

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