Showing papers on "Bessel filter published in 2000"
TL;DR: It is shown 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.
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.
24 citations
30 Apr 2000
TL;DR: A functional approach for fault modeling in 2nd order filters is presented and the transient response method is used for fault detection, using the transient analysis of simple input test vectors.
Abstract: This work proposes a new BIST scheme for 2nd order Butterworth, Chebyshev and Bessel filter approximations, using the transient analysis of simple input test vectors. A functional approach for fault modeling in 2nd order filters is presented and the transient response method is used for fault detection. The approach considers the filter as a 2nd order dynamic system where /spl omega/c and Qp deviations are faults to be detected. The peak time is the observed parameter that is evaluated in order to verify the filter correctness. The obtained results are very promising since all of /spl omega/c and Qp deviations as well as 100% of passive components are detected for this BIST scheme.
23 citations
TL;DR: In this article, a pattern synthesis of linear antennas utilizing the spherical Bessel functions is presented, which leads to antenna current distribution by the Legendre polynomials of the first kind, which are of finite support.
Abstract: Pattern synthesis of linear antennas utilizing the spherical Bessel functions is presented. This leads to antenna current distribution by the Legendre polynomials of the first kind, which are of finite support. Some examples are given to illustrate this procedure.
20 citations
TL;DR: In this article, a reasonable quality factor governing the axial intensity behavior of a phase-undistorted truncated Bessel beam is found to be the inverse square root of the Fresnel number defined, for a given aperture, from the axially point of geometrical shadow.
Abstract: Approximate analytic expressions are obtained for evaluating the axial intensity and the central-lobe diameter of J0 Bessel beams transmitted through a finite-aperture phase filter. A reasonable quality factor governing the axial-intensity behavior of a phase-undistorted truncated Bessel beam is found to be the inverse square root of the Fresnel number defined, for a given aperture, from the axial point of geometrical shadow. Additional drastic reduction of axial-intensity oscillations is accomplished by using marginal phase correction of the beam instead of the well-known amplitude apodization. A procedure for analytically calculating an optimal monotonic slowly varying correction phase function is described.
20 citations
TL;DR: The theory indicates that for an nth-order Besselbeam, the second-harmonic beam is nearly diffraction-free in the radial direction and behaves as a Bessel beam of the order 2n, and that the axial pressure amplitude is proportional to the square root of propagation distance.
Abstract: We investigate the second-harmonic generation of the nth-order Bessel beam in the nonlinear medium. The analysis is based on the Khokhlov-Zabolotskaya-Kuznetsov wave equation under the second-order approximation in nonlinear acoustics. The theory indicates that for an nth-order Bessel beam, the second-harmonic beam is nearly diffraction-free in the radial direction and behaves as a Bessel beam of the order 2 n, and that the axial pressure amplitude is proportional to the square root of propagation distance. A variety of applications in many fields of nonlinear acoustics and nonlinear optics is expected.
13 citations
01 Feb 2000
TL;DR: In this article, an integrated delay cell for a disc-drive read channel has been designed to combine a high 120 MHz bandwidth with a low power dissipation and a large 1:6 tuning range.
Abstract: An integrated delay cell for a disc-drive read channel has to combine a high 120 MHz bandwidth with a low power dissipation and a large 1:6 tuning range. Because of linearity and transfer requirements, the implementation is a continuous-time third-order Bessel allpass filter. An opamp-MOSFET-C configuration is best for low power consumption but has two problems: a small tuning range and often a low bandwidth. The author gives solutions to both problems, including a patented tuning-range extension circuit. Measurements show that the design method works well. The cell dissipates 15 mW at 27°C.
9 citations
TL;DR: In this article, the relativistic expressions for energy and momentum were derived for a continuous time, one-dimensional discrete jump process from two inertial frames with a relative constant velocity.
Abstract: The recursive formulas of modified Bessel functions give the relativistic expressions for energy and momentum. Modified Bessel functions are solutions to a continuous time, one-dimensional discrete jump process. The jump process is analyzed from two inertial frames with a relative constant velocity; the average distance of a particle along the chain corresponds to the distance between two observers in the two inertial frames. The recursion relations of modified Bessel functions are compared to the ‘ calculus’ which uses the radial Doppler effect to derive relativistic kinematics. The Doppler effect predicts that the frequency is a decreasing function of the velocity, and the Planck frequency, which increases with velocity, does not transform like the frequency of a clock. The Lorentz transformation can be interpreted as energy and momentum conservation relations through the addition formula for hyperbolic cosine and sine, respectively. The addition formula for the hyperbolic tangent gives the well-known relativistic formula for the addition of velocities. In the non-relativistic and ultra-relativistic limits the distributions of the particle’s position are Gaussian and Poisson, respectively.
7 citations
15 Oct 2000
TL;DR: In this paper, an analog signal processor was developed to achieve the best compromise between energy and time resolution, low noise, and low cost for the Pierre Auger cosmic ray observatory.
Abstract: The fluorescence detector of the Pierre Auger Cosmic Ray Observatory will provide a measurement of the parameters of extended air showers in the range from 10/sup 19/ to 10/sup 21/ eV. An array of 20/spl times/22 photomultiplier tubes (PMTs) is placed at the focal surface of a large-aperture telescope thus forming one of the 30 detector modules. The shape of the signal generated by each PMT is variable, depending mostly on the geometry of the air shower as seen by the detector; after analog processing the waveforms will be sampled at a rate of 10 MHz with 12 bit resolution. We have developed an analog signal processor to achieve the best compromise between energy and time resolution, low noise, and low cost. The head electronics provides an active bias network for the PMTs, which keeps the gain constant even in the presence of large dc background light from the night sky. This dc level is measured by means of a built-in optocoupled linear circuit. The pulse signal is sent through a twisted pair to the analog front-end board. At this stage a compression of the 15-bit dynamic range of the signal into the 12-bit range of the FADC is performed. Antialiasing is provided by a Bessel filter.
5 citations
TL;DR: The closed-form expressions of the Laplace transforms of ordinary Bessel functions of an evev order can be found in standard compilations for the cases n=0 and b=0 only as mentioned in this paper.
Abstract: Closed-form expressions of the Laplace transforms of ordinary Bessel functions , of an evev order can be found in standard compilations for the cases n=0 and b=0 only. Investigations of the Sommerfeld description of inhomogeneous spherical waves led to two such forms, one in terms of modified spherical Bessel functions, and another one involving incomplete gamma funtions.
3 citations
Patent•
28 Jun 2000
TL;DR: In this article, two or more triangular apertures are employed to pass radiation from a source to a detector to reduce the amount of stray radiation received by the detector, and a Bessel filter is employed to reduce effect of flicker and other rapid changes in intensity in the radiance from the source.
Abstract: Two or more triangular apertures are employed to pass radiation from a source to a detector to reduce the amount of stray radiation received by the detector Preferably, the two apertures are equilateral triangles oriented at 60° rotated relative to each other and have dimensions proportional to their distances from the sensor A Bessel filter is employed to reduce the effect of flicker and other rapid changes in intensity in the radiance from the source The output of the sensor is integrated and sampled at sampling time intervals that are powers of two of time, and a reading is provided when the output of the integrator exceeds the same threshold under all radiation source intensity conditions so that the meter has a substantially constant resolution at different signal levels
3 citations
03 May 2000
TL;DR: In this article, a method of finding the zero points and dividing the intervals is used to compute the integral of double Bessel function, and the errors of these two algorithms are discussed.
Abstract: Using the integral equation method, the integral computation of the primary field of the 3-D electromagnetic scattering problem in the earth half space is an integral of double Bessel functions. The dipole model is usually taken for its numerical computation. The integral with integrand of double Bessel function is simplified to the integral of single Bessel function and is computed with the Hankel transformation. In this paper. A method of finding the zero points and dividing the intervals is used to compute the integral of double Bessel function. Taking different integral parameters, the integral results of double Bessel function are compared with those of single Bessel function with Hankel transformation. The errors of these two algorithms are discussed.
TL;DR: In this article, a design procedure is proposed for a filter with an integrator configuration in which the frequency deviation is small even if the frequency characteristic of the functional circuit deviates from the ideal one due to the parasitic elements in the circuit.
Abstract: The integrator configuration is a filter configuration method involving realization of operational function of each edge by the functional circuits of an integrated circuit based on the signal flow graph with the desired frequency characteristics, and can realize an arbitrary linear time-invariant continuous time system filter. In this paper, a design procedure is proposed for a filter with an integrator configuration in which the frequency deviation is small even if the frequency characteristic of the functional circuit deviates from the ideal one due to the parasitic elements in the circuit. In general, when the integration edge has a feedback edge to return its output to its own input in the signal flow graph, the integration edge and the feedback edge can be realized with ideal lossy integrators on the integrated circuit. Hence, there is a degree of freedom in realization of the integration edge with feedback to itself. In the proposed method, this degree of freedom is fully utilized to reduce the frequency deviation. The equation to evaluate the characteristic deviation by the parasitic elements is derived, and the parameter to express the degree of freedom is determined such that this deviation is reduced. As an application example, a third-order Bessel filter is designed. Its numerical simulation is used for confirming the effectiveness of the proposed method. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(6): 50–60, 2000