Lowpass filters approximation based on the Jacobi polynomials

Author:

Stojanovic Nikola1,Stamenkovic Negovan2

Affiliation:

1. Faculty of Electronic Engineering, Niš

2. Faculty of Natural Science and Mathematics, Priština

Abstract

A case study related to the design the analog lowpass filter using a set of orthogonal Jacobi polynomials, having four parameters to vary, is considered. The Jacobi polynomial has been modified in order to be used as a filter approximating function. The obtained magnitude response is more general than the response of the classical ultra-spherical filter, due to one additional parameter available in orthogonal Jacobi polynomials. This additional parameter may be used to obtain a magnitude response having either smaller passband ripple, smaller group delay variation or sharper cutoff slope. Two methods for transfer function approximation are investigated: the first method is based on the known shifted Jacobi polynomial, and the second method is based on the proposed modification of Jacobi polynomials. The shifted Jacobi polynomials are suitable only for odd degree transfer function. However, the proposed modified Jacobi polynomial filter function is more general but not orthogonal. It is transformed into orthogonal polynomial when orders are equal and then includes the Chebyshev filter of the first kind, the Chebyshev filter of the second kind, the Legendre filter, Gegenbauer (ultraspherical) filter and many other filters, as its special cases.

Publisher

National Library of Serbia

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Comparative performance of some polynomial-based lowpass filters for microwave/digital transmission applications;International Journal of Electronics;2018-07-17

2. New flat pass-band of low-pass responses with varying attenuation in stop-band;Proceedings of the 3rd International Conference on Communication and Information Processing - ICCIP '17;2017

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