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Showing papers on "Bessel filter published in 1968"


Journal ArticleDOI
TL;DR: In this paper, Gray et al. proposed a new rational approximation to the Mills' ratio, which is a limiting case of the G-transformation, and used it for digital computers.
Abstract: 1. R. G. Hart, \"A close approximation related to the error function,\" Math. Comp., v. 20, 1966, pp. 600-602. 2. H. L. Gray, \"A limiting case of the G-transformation,\" SIAM J. Numer. Anal. (To appear.) 3. H. L. Gray & W. R. Schucany, \"A new rational approximation to Mills' ratio,\" /. Amer. Statist. Assoc. (To appear.) 4. C. Hastings, Approximations for Digital Computers, Princeton Univ. Press, Princeton, N. J., 1955, p. 167. MR 16, 963.

10 citations


Journal ArticleDOI
01 Jan 1968
TL;DR: In this paper, a method for determining the transfer functions of phase-corrective networks of both minimum-phase and all-pass types is presented, based on manipulation of a class of polynomials containing one or more variable parameters.
Abstract: A method is presented for determining the transfer functions of phase-corrective networks of both minimum-phase and all-pass types. The method is based on manipulation of a class of polynomials containing one or more variable parameters, which is derived from Bessel polynomials and represents basically an extension of the application of Bessel polynomials and related Bessel functions to solving the problem of approximation to the ideal constant-group-delay characteristic. Some simple phase-correcting networks, useful in those applications where the phase distortion occurs mainly at high frequencies, are first discussed, and the formulas and graphs for the evaluation of their group-delay responses are given. The extension of the method to allow for determination of the transfer function of the correcting network matching a prescribed phase characteristic is then presented. Both maximally fiat and equal-ripple types of approximation are considered, and explicit formulas for the evaluation of the coefficients of transfer functions of order n<6 are derived. The conditions on which the order of equalisation can be increased without affecting the complexity of the correcting network are also stated explicitly.

5 citations


Journal ArticleDOI
01 Jul 1968
TL;DR: In this paper, a simple formula is derived for transforming the slowly convergent series involving Bessel functions which arise in axially symmetric potential problems into more rapidly convergent ones, using it, sums of series previously found by elaborate special methods may be obtained by direct substitution.
Abstract: A simple formula is derived for transforming the slowly convergent series involving Bessel functions which arise in axially symmetric potential problems into more rapidly convergent series. Using it, sums of series previously found by elaborate special methods may be obtained by direct substitution. The necessary numerical coefficients are given.

2 citations



Journal ArticleDOI
TL;DR: In this paper, the Bessel function of the first kind and order v, jvk its kth positive zero and jv, 0 = 0, was proved to be a Bessel Function.
Abstract: In accordance with customary notation, Jv(t) denotes the Bessel function of the first kind and order v, jvk its kth positive zero and jv, 0 = 0.The object of this note is to prove that

1 citations