A chebyshev rational function with low Q‐factors

Abstract

SUMMARYThe presented rational function is a modification of a recently published Chebyshev rational function defined by means of some orthogonal polynomials. The necessary conditions providing for the lowest pole Q-factors for a given ripple are found. The function is a ratio of two similar Chebyshev polynomial transfer functions with multiple poles.The selectivity of the function can be increased by using the Chebyshev rational characteristic function instead of the characteristic polynomials. The minimum number of active elements in the cascade connection is obtained with third-order elliptic characteristic functions.The function is compared with the Cauer (elliptic) and MCPER filters. The distinctive features of the presented function are small Q-factors of the poles, almost ideal dynamic range, simple design and poles with the same multiplicity rn, where m designates the number of cascaded blocks

Efficient Multirate EMQF Digital Filters

“…The technique was formerly suggested for continuous-time filter design [3] so that very selective filters can be implemented with low Q factors. Filters with lower Q factors are more robust for implementation and are less sensitive to element changes due to temperature variations and finite element tolerances.…”

A new approach to the phase error and THD improvement in linear phase IIR filters

“…Therefore, a damping factor could be improved by appropriate selection of transfer function H ( z ) . In this paper, it is shown that a Chebyshev rational function [4] based on analog prototype of elliptic filters with minimal &-factors [5] results in improvement of the phase error. Instead of the 7th-order elliptic transfer function given in [I] A ( z ) = B ( z ) = 0.18 + 0.825%-' + 1 .…”

“…7 8 4 r 5 + 0.258z-" + 0 . 0 2 5 3~-~, a new 15th-order transfer function is derived as cascade connection of two fifth-order minimum Q-factor analog prototype elliptic filters [5] and one fifth order filter with complex zeros [4]: The magnitude response is shown in Fig. 6.…”