Showing papers on "Bessel filter published in 1971"
TL;DR: In this article, a solution obtained by a direct approximation procedure in the z plane is presented, where the denominator of the transfer function turns out to be a Gaussian hypergeometric function, connected with the Legendre functions.
Abstract: A well-known limitation of the recursive digital filter, when compared to the nonrecursive filter, is its incapability of having a strictly linear phase characteristic; thus it may only approximate a constant group delay. For the analog filters the choice of the maximally flat criterion leads to the use of the Bessel polynomials. Yet digital approximations of these continuous filter functions are inadequate to yield the true maximally flat delay approximation of the recursive filters. Our purpose is to provide for the problem at hand a solution obtained by a direct approximation procedure in the z plane. The denominator of the transfer function turns out to be a Gaussian hypergeometric function, more particularly connected with the Legendre functions. The stability of the filters is discussed and some numerical results in regard to the amplitude and phase responses as well as the pole loci are given.
247 citations
TL;DR: In this article, the roots of low-pass Bessel and Butterworth transfer functions in both Cartesian and polar form are given for the orders 1 through 30 inclusive, and group delay characteristics for each of the above orders are tabulated for both the Bessel transfer functions and the Butterworth functions.
Abstract: Tables are given for the roots of the normalized low-pass Bessel and Butterworth transfer functions in both Cartesian and polar form. The latter form is especially useful when designing transitional (Butterworth-Thomson) functions. The tables cover the orders 1 through 30 inclusive. In addition, the group delay characteristics for each of the above orders are tabulated for both the Bessel and Butterworth functions.
5 citations
01 Mar 1971
3 citations
TL;DR: In this article, a parametric constraint for a general, second-order, linear, non-autonomous system to possess responses expressible in terms of the well-known Bessel functions is presented.
Abstract: A parametric constraint for a general, second-order, linear, non-autonomous system to possess responses expressible in terms of the well-known Bessel functions is presented. In effect, this paper develops a process of synthesis (of systems with a Bessel typo of responses) which can be programmed using algebraic languages to obtain a practical tool of study.
1 citations
TL;DR: In this article, the authors discuss two extensions to previous work which may speed up, and render more accurate, the evaluation of the Bessel function, i.e., real recursion for complex argument and the suppression of overflows.
Abstract: The author discusses two extensions to previous work which may speed up, and render more accurate, the evaluation of the Bessel function. These extensions are real recursion for complex argument and the suppression of overflows.
1 citations