Showing papers on "Bessel filter published in 1977"

Transfer functions of generalized Bessel polynomials

Abstract: The stability and approximation properties of transfer functions of generalized Bessel polynomials (GBP) are investigated. Sufficient conditions are established for the GBP to be Hurwitz. It is shown that the Pade approximants of e^{-s} are related to the GBP. An infinite subset of stable Pade functions useful for approximating a constant time delay is defined and its approximation properties examined. The low-pass Pade functions are compared with an approximating function suggested by Budak. Basic limitations of Budak's approximation are derived.

Lower bounds for the zeros of Bessel functions

Abstract: Let jp „ denote the nth positive zero of J , p > 0. Then / ■■> 7\'/2 Jp.n > Oln + P) ■ We begin by considering the eigenvalue problem (1) -(•*/)' + x~y = X2x2p-Xy, X,p>0, (2) y(a) =y(\) = 0, 0 < a < 1. For simplicity of notation we will set q = p~x. It is easily verified that the general solution of (1) is y(x) = CxJq(Xqxx/q) + C2Yq(Xqxx'q) and that the eigenvalues are given by Jq(Xq)Yq(Xqax/q) Jq(Xqax/q)Yq(Xq) = 0. If zn(a, r) denotes the «th positive zero of Jr(z)Yr(zax/q) Jr(zax/q)Yr(z) = 0, then the «th eigenvalue, X2(a), of (1), (2) is given by (3) X2(a) = (z„(a, q)/qf. Let jrn denote the «th positive zero of Jr. On p. 38 of [4] it is shown that zn(a, r) —>jrn as a —> 0+ whenever r is a positive integer. The restriction on r is extrinsic so that (4) Mm zn(a,r)=jrn, r > 0. a—»0"1" Let R [p, y] denote the Rayleigh quotient R[p,y] = f\-(xy')' + x~xy)y dx / f\2p-xy2 dx. Ja Ja It is well known that the eigenvalues {X2(p)} of (1), (2) can be obtained from the Rayleigh quotient [5]. Let V denote the linear space of all functions in C2((a, 1)) which satisfy the boundary conditions (2). Then X2(p)= min R[p,y]y£ y,y=^o Let^,,^, . . . ,y„ be « functions in V, A denote the subspace of V spanned by yvy2, . . . ,yn and A x denote the orthogonal complement of A relative to V. Then Received by the editors January 5, 1976 and, in revised form, September 13, 1976. AMS (MOS) subject classifications (1970). Primary 33A40. © American Mathematical Society 1977 101 License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use

Bessel function type automatic delay equalizer

Abstract: A Bessel function type automatic delay equalizer comprising a plurality of transversal filters each of which has an independent delay cosine equalization component having a predetermined period, and the superposition of those filters providing the desired characteristics, characterized in that, said equalizer further comprises a Bessel function generator for controlling the tap gain of said transversal filters

Generalized bessel polynomials with application to the design of bandpass filters with approximately flat group delay response

Abstract: The continued fraction expansion of the ordinary Bessel polynomials is modified by replacing the complex frequency variable p by p/(1+γp), where γ=⩾0. The resulting polynomials, when a reactance transformation is applied, are capable of providing bandpass filters with an approximately flat group delay response.

The evaluation of generator coordinate amplitudes

Abstract: A method is outlined which enables one to calculate generator coordinate amplitudes using a series expansion that employs spherical Bessel functions. The method is illustrated for the case of the collision of alpha particles with 6Li nuclei.