LOWPASS FILTERS APPROXIMATION BASED ON THE ORTHOGONAL JACOBI POLYNOMIAL

Nikola Stojanovic, Negovan Stamenkovic

DOI Number
10.2298/FUEE1703351S
First page
351
Last page
362

Abstract


A case study related to the design the 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 ultraspherical 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. It 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.


Keywords

Filters, analog circuits, approximation, filter characteristic functions, Jacobi polynomial, orhogonal polznomials

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