Showing papers on "Bessel filter published in 2007"

Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights

Abstract: We study a model of $n$ non-intersecting squared Bessel processes in the confluent case: all paths start at time $t = 0$ at the same positive value $x = a$, remain positive, and are conditioned to end at time $t = T$ at $x = 0$. In the limit $n \to \infty$, after appropriate rescaling, the paths fill out a region in the $tx$-plane that we describe explicitly. In particular, the paths initially stay away from the hard edge at $x = 0$, but at a certain critical time $t^*$ the smallest paths hit the hard edge and from then on are stuck to it. For $t eq t^*$ we obtain the usual scaling limits from random matrix theory, namely the sine, Airy, and Bessel kernels. A key fact is that the positions of the paths at any time $t$ constitute a multiple orthogonal polynomial ensemble, corresponding to a system of two modified Bessel-type weights. As a consequence, there is a $3 \times 3$ matrix valued Riemann-Hilbert problem characterizing this model, that we analyze in the large $n$ limit using the Deift-Zhou steepest descent method. There are some novel ingredients in the Riemann-Hilbert analysis that are of independent interest.

Zeros of the Bessel and spherical Bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering

Abstract: Some novel interlacing properties of the zeros for the Bessel and spherical Bessel functions are first presented and then applied to prove an interesting uniqueness result in inverse acoustic obstacle scattering. It is shown that in the resonance region, the shape of a sound-soft/sound-hard ball in R 3 or a sound-soft/sound-hard disc in R 2 is uniquely determined by a single far-field datum measured at some fixed spot corresponding to a single incident plane wave.

Bessel harmonic analysis and approximation of functions on the half-line

Abstract: We study problems of approximation of functions on? in the metric of? with power weight using generalized Bessel shifts. We prove analogues of direct Jackson theorems for the modulus of smoothness of arbitrary order defined in terms of generalized Bessel shifts. We establish the equivalence of the modulus of smoothness and the -functional. We define function spaces of Nikol'skii-Besov type and describe them in terms?of best approximations. As a?tool for approximation, we use a?certain class of entire functions of exponential type. In this class, we prove analogues of Bernstein's inequality and others for the Bessel differential operator and its fractional powers. The main tool we use to solve these problems is Bessel harmonic analysis.

Selected Structures of Filters With Time-Varying Parameters

Abstract: One important problem of signal processing in measurement systems is designing a filter that possesses a linear-phase response and, at the same time, has a short transient state. This paper presents the methodology of varying, in the time parameters, a low-pass Bessel filter and a filter of a constant component. In the proposed filters, significant shortening of the transient state is achieved at the cost of a slight increase in oscillations. This paper also addresses the problems that are connected with continuous running of the filters with varying parameters. The presented approach allows better preservation of the edge shape, as compared with traditional filtering techniques. Typical filtering results are presented, which are obtained by simulations of selected structures of filters with varying parameters.

Standard Stars for Linear Polarization Observed with FORS1

Abstract: We present the analysis of the observations of standard stars for linear polarization obtained from 1999 to 2005 within the context of the calibration plan of the FORS1 instrument of the ESO VLT. We have considered observations carried out both in imaging polarimetric and in spectropolarimetric mode. Broadband polarization was obtained in the Bessel BV RI filters; spectropolarimetry was obtained with various grisms covering different optical ranges and with a typical resolution of a few hundreds. Spectropolarimetric data have been convolved with the transmission functions of the Bessel filters, which enabled us to calculate polarization values equivalent to broadband polarization measurements in imaging mode. Finally, for each star, instrument mode, and for each Bessel filter band, we have calculated an average polarization value obtained after filtering all available data with a kσ-clipping algorithm.

Current-Mode LP CMOS Active Filter for Very Low Frequency Applications

Abstract: A new structure of a current-mode LP active filter in CMOS technology, suitable for applications in very low frequency filters is presented in the paper. On the basis of this structure, particular solution of a sixth-order Bessel filter has been designed and tested by SPICE simulations. The main features of this design are; very low cutoff frequency (2.4 Hz), very low dissipation power (9 nW) and low supply voltage (1 V with additional auxiliary supply voltage equal to -1 V).

10-Gb/s Slow-light Performance Based on SBS Effect in Optical Fiber using NRZ and PSBT Modulation Formats

Abstract: For the first time, we have demonstrated error-free operation of slow-light via SBS in optical fiber for 10-Gb/s NRZ and PSBT formats The PSBT signal sensivity is 52dB better than the NRZ case for a 35-ps delay Introduction Recently, slow-light has attracted much interest due to potential applications in future optical networks, such as optical buffering and tunable time delay Among all proposed techniques, slow-light mechanism based on Stimulated Brillouin Scattering (SBS) in optical fibre has attracted extensive attention [1-4] The problem of narrow-band SBS gain has been solved by direct modulation of a pump laser diode using a Gaussian noise source [2] Until now, the system performance for 10-Gb/s signal transmitted in SBS based slow-light have been investigated only in case of differential-phase-shiftedkeying (DPSK) modulation format [3] However, the sensitivity was degraded by ~10dB for a 42-ps delaytime due to SBS filtering effect and chromatic dispersion accompanied with slow-light In this paper, we investigate the system performance of 10-Gb/s non-return-to-zero (NRZ) and phaseshaped binary transmission (PSBT) modulation formats in SBS based slow-light delay line It is well-known that PSBT format allows high spectral efficiency and strong dispersion-tolerance [5] Here, we propose to utilize the PSBT format to reduce the signal distortions in slow-light All the results in term of sensitivity and power penalty have been measured at a bit-error-rate (BER) of 10 For the 10-Gb/s PSBT signal, a negative power penalty, ie -2 dB for a 25 ps delay-time, has been obtained When the delay-time is increased to 35 ps, the sensitivity of the PSBT signal is 52 dB better than the NRZ signal case Maximum of ~50 ps delay with error-free operation can be obtained only by using PSBT format Experimental setup Fig1 depicts the experimental set-up The signal transmitter consists of a laser diode (LD1) operating at 154826nm, and a Mach-Zehnder modulator (MZM) driven by a 10-Gb/s pseudo-random bit sequence (PRBS) A 10-Gb/s PBST modulation format can be achieved by filtering the electrical NRZ signal using a 5 order Bessel filter with a ~27GHz cut-off frequency [6] A 2-1 word length sequence is used for BER measurements due to non-optimized 3-GHz PSBT electrical filter and the driver [7] The inset of Fig1 corresponds to the eye diagram of the PSBT signal The signal is launched into a 20-km long Truewave (TW) fibre with a ~1075GHz Brillouin frequency shift The SBS pump source is a directly modulated laser diode (LD2), whose central wavelength can be precisely controlled by temperature The pump LD is modulated by a Gaussian noise source (Tektronix AFG3252), and subsequently boosted by a high power erbium-doped fibre amplifier (EDFA) We have obtained ~12GHz SBS pump bandwidth, resulting in ~7GHz gain bandwidth for a 22-dBm pump power

Bessel Filter implementation in Log-Domain

Abstract: In signal processing, mainly in audio domain, the need for a linear phase characteristic is sometimes more important than the frequency specifications concerning the pass band and stop bandwidth. For these applications, we need a Bessel approximation for the frequency characteristics. If the application is designed for portable devices low power and low voltage building blocks are also required. Log-Domain circuits may be very suitable. We propose and analyze in this paper a log-domain 4 th order Bessel filter and emphasize its performance in comparison with an AO-RC design.

Solution of characteristic equation in eigenvalue problems of spherical Bessel equation by using Matlab algorithm

Abstract: The characteristic equation in common eigenvalue problems of spherical Bessel equation on the interval of was given.The spherical Bessel function was transformed into a cylindrical one by using the dependent relation of semi-odd-ordered Bessel function and Bessel function to each other,resulting in an eigenvalue and eigenfunction of the spherical Bessel equation on general intervals.Aimed at the different cases of high-order and low-order spherical Bessel function,the solution procedure for obtaining the roots of characteristic equation with Matlab programming was discussed and its practical application was introduced,also.

Complete LC Ladder Bessel Filter Tabulation

Abstract: Bessel filter has been widely used in industry for analog filter circuit design with its maximally flat time-delay or least group delay ripple performance. Nevertheless, there has been only one set of tabulation per order (LC element number) available for the realization of a specific Bessel filter through LC ladder architecture in conventional literature. To synthesize a LC ladder Bessel filter thoroughly, especially for higher order and more tabulations concerns, the problem of calculation accuracy should be precisely concerned to avoid neglecting the relatively significant but smaller coefficient values. In this paper we have obtained a complete set of tabulation per order, which can be generalized as 2[(n+2)/2] for an nth order LC ladder Bessel filter network with duality being included.

Modeling Delays of Microwave Transistors and Transmission Lines by the 2nd Order Bessel Function

Abstract: At present, most of simulation programs can characterize gate delays of microwave transistors. How- ever, the delay is mostly approximated by means of first- order differential equations. In the paper, a more accurate way is suggested which is based on an appropriate s order differential equation. Concerning the transmi ssion line delay, majority of the simulation programs use both Branin (for lossless lines) and LCRG (for lossy lin es) mod- els. However, the first causes extreme simulation t imes, and the second causes well-known spurious oscillations in the simulation results. In the paper, an unusual way fo r mod- eling the transmission line delay is defined, which is also based on the second-order Bessel function. The prop osed model does not create the spurious oscillations and the simulation times are comparable with those obtained with the classical models. Properties of the implementat ion of the second-order Bessel function are demonstrated b y analyses of both digital and analog microwave circu its.

Selected Structures of Filters With

Abstract: One important problem of signal processing in mea- surement systems is designing a filter that possesses a linear-phase response and, at the same time, has a short transient state. This pa- per presents the methodology of varying, in the time parameters, a low-pass Bessel filter and a filter of a constant component. In the proposed filters, significant shortening of the transient state is achieved at the cost of a slight increase in oscillations. This paper also addresses the problems that are connected with continuous running of the filters with varying parameters. The presented ap- proach allows better preservation of the edge shape, as compared with traditional filtering techniques. Typical filtering results are presented, which are obtained by simulations of selected structures of filters with varying parameters.

Evaluation of Bessel Functions Using a Computer Program

Abstract: In cylindrical coordinate, there are two types of Bessel functions. These functions are the Bessel function and the modified Bessel function. Both functions are expressed mathematically by infinite power series, and each one consists of different orders, beginning with the zero -order, and then the first order, the second order, and so on. The Bessel function is the solution of the Bessel differential equation, which is a l inear, second-order ordinary differential equation. Similarly, the modified Bessel function is the solution of modified Bessel differential equation. The difference between these two differential equations is the signs of the non -differential terms. The applications of Bessel functions are in the scientific areas of elasticity, electrical field theory, aerodynamic flutter analysis, fluid flow, and heat transfer by conduction. An executable computer program has been developed in this study for the numerical computation of the Bessel function and the modified Bessel function. This program is called BESSEL.EXE. It is distributed free by contacting the author through his e -mail address. Keyword: Bessel functions, modified Bessel functions, computer program.