Bessel filter

About: Bessel filter is a research topic. Over the lifetime, 656 publications have been published within this topic receiving 16808 citations.

A 1-V CMOS log-domain integrator

Abstract: A novel circuit implementation of a CMOS log-domain integrator is presented. Unlike most other implementations, it does not require placing of MOSFETs in separated wells, and therefore allows very compact filters, which are fully compatible with modern standard CMOS technologies. Besides the saving of chip area, this also helps to reduce parasitic capacitances. The most important advantage of this circuit is the very low minimum required supply voltage of only two saturation voltages plus one gate-to-source voltage of a weakly inverted MOSFET. This is fully compatible with the minimum required supply voltage of digital gates implemented in the same technology. The integrator was used as a building block for a 5th-order Bessel filter, which was simulated with the transistor parameters of a 0.5 /spl mu/m CMOS technology.

The second harmonic component in the Bessel beam

Abstract: The analysis is based on the Khokhlov–Zabolotskaya–Kuznetsov wave equation. Analytical and approximate solutions are derived for the second harmonic component in the Bessel nondiffracting beam. The theoretical results indicate that the second harmonic beam is nearly nondiffracting in the radial direction and the pressure amplitude is proportional to the square root of propagation distance in the quasilinear approximation, and that the beamwidth of the second harmonic is just 1/2 times that of the fundamental component in the Bessel field, not as 1/√2 times in the fields radiated by other sources.

Circuit technique that sets transconductance

Abstract: A fast parasitic-insensitive continuous-time filter and equalizer integrated circuit that uses an active integrator is described. Circuit techniques for excess-phase cancellation, and for setting the corner-frequency of the filter and equalizer are also described. These techniques result in a filter and equalizer chip with performance independent of process, supply, and temperature without employing phase-lock loops. This 20MHz 6th order Bessel filter and 2nd order equalizer operate from 5V, and generate only 0.24% (-52dB) of total harmonic distortion when processing 2Vp-p differential output signals. The device is optimized to limit high-frequency noise and to amplitude equalize the data pulses in hard disk read-channel systems. The device supports data rates of up to 36Mbps, and is built in a 1.5 μ/4GHz BiCMOS technology.

Accurate computation of the zeros of the generalized Bessel polynomials

Abstract: A general method for approximating polynomial solutions of second-order linear homogeneous differential equations with polynomial coefficients is applied to the case of the families of differential equations defining the generalized Bessel polynomials, and an algorithm is derived for simultaneously finding their zeros. Then a comparison with several alternative algorithms is carried out. It shows that the computational problem of approximating the zeros of the generalized Bessel polynomials is not an easy matter at all and that the only algorithm able to give an accurate solution seems to be the one presented in this paper.

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