Showing papers on "Bessel filter published in 2012"

Generation of Propagating Bessel Beams Using Leaky-Wave Modes

Abstract: The generation of Bessel beams using a leaky radial waveguide is presented. The radial waveguide consists of a capacitive sheet over a ground plane. It supports an azimuthally invariant leaky-wave mode whose normal electric-field component is a truncated, zeroth-order Bessel function. The annular spectrum and nondiffractive extent of the Bessel beam is clearly linked to the complex wavenumber of the leaky-wave mode. The fields inside the radial waveguide are derived using classical vector potential techniques. A vector approach is employed to avoid paraxial approximations of earlier works and the associated limitations on shaping the Bessel beam. Design rules are provided to synthesize a desired propagating Bessel beam. A simple coaxial feed is proposed for the radial waveguide and its input impedance is derived analytically. The analytical results are also validated numerically. The proposed structure and design procedure can be used for generating arbitrary zeroth-order propagating Bessel beams at microwave and millimeter-wave frequencies.

Fundamental solutions of singular differential equations with a bessel D B operator

Abstract: We prove a theorem on the fundamental solution of an ordinary differential equation in which the role of even-order derivatives is played by powers of the Bessel operator and the role of odd-order derivatives is played by the derivatives of integer powers of the Bessel operator. The result obtained has allowed us to derive formulas for the fundamental solutions of classical singular equations with the Bessel operator when the index of the Bessel operator can take negative values greater than −1; in this case the dimension N of the Euclidean space and the total sum |γ| of the indices of the Bessel operators that appear in the equation should satisfy the condition N + |γ| − 1 > 0.

Edge Detection Filter based on Mumford-Shah Green Function

Abstract: In this paper, we propose an edge detection algorithm based on the Green function associated with the Mumford-Shah segmentation model. This Green function has a singularity at its center. A regularization method is therefore proposed here to obtain an edge detection filter known here as the Bessel filter. This filter is robust in the presence of noise, and its implementation is simple. It is demonstrated here that this filter is scale invariant. A mathematical argument is also provided to prove that the gradient magnitude of the convolved image with this filter has local maxima in discontinuities of the original image. The Bessel filter enjoys better overall performance (the product of the detection performance and localization indices) in Canny-like criteria than the state-of-the-art filters in the literature. Quantitative and qualitative evaluations of the edge detection algorithms investigated in this paper on synthetic and real world benchmark images confirm the theoretical results presented here, indicating the scale invariant property of the Bessel filter. The numerical complexity of the algorithm proposed here is as low as any convolution-based edge detection algorithm.

Stokes polynomial filters

Abstract: The paper considers a new class of filters with transfer functions using the polynomials introduced by the British physicist Sir G.G. Stokes. The filters are transitional between Bessel and Butterworth ones. When one compares the step-responses of Bessel, Stokes, and Butterworth filters of the same order and the same −3dB bandwidth then the result is following. The Bessel filters have a certain delay and (practically) no overshoot in their step-transient response. The Stokes filters have larger delay than Bessel filters and a small overshoot. Finally, the Butterworth filters have largest delay and largest overshoot. The paper illustrates these properties and describes the data required for synthesis of the Stokes filters.

Comparison of High-Order Harmonic Generation of Ar Using a Truncated Bessel or a Gaussian Beam

Abstract: As discussed in Chap. 3, a full quantitative description of high-order harmonic generation (HHG) in a macroscopic medium requires the inclusion of the propagation of fundamental laser field and generated harmonic field. The QRS theory has been successfully incorporated into the well-established macroscopic propagation theory such that simulated HHG spectra can be compared directly with the experimental measurements in Fig. 3.3, where the experimental conditions have been well specified. High harmonics in these studies were generated with multi-cycle (FWHM, \(\sim \)10 optical cycles) laser pulses. And these simulations were based on the assumption that the initial fundamental laser pulse at the entrance of gas medium was a Gaussian beam. Few-cycle laser pulses are also widely used to produce high harmonics, and they are usually obtained by gas-filled hollow-core fiber compression technique [1]. In this method, an incident laser beam can be dominantly coupled into the fundamental EH\(_{11}\) hybrid mode by proper mode matching. At the exit of the fiber a truncated Bessel (TB) beam is produced instead of a Gaussian beam. Nisoli et al. [2] have shown that using a TB beam as the driving laser pulse the spatial properties (divergence and brightness) of high harmonics were greatly improved. To simulate high harmonics generated by few-cycle pulses, the macroscopic propagation code is generalized to include the conditions where the spatial distribution of generating laser pulse is a TB beam.

Experimental generation of propagating Bessel beams with a low-profile leaky radial waveguide

Abstract: The generation of Bessel beams using a leaky radial waveguide is presented. The radial waveguide consists of a capacitive sheet over a ground plane. It supports an azimuthally invariant leaky-wave mode whose normal electric-field component is a truncated, zeroth-order Bessel function. A vector field approach is employed to derive design relations for the radial waveguide, in contrast to previous works on Bessel beams based on scalar wave theory. A prototype is presented. Electric field measurements and their respective Fourier transforms validate the operation of the prototype as a Bessel-beam launcher. The proposed structure can be used for generating arbitrary zeroth-order propagating Bessel beams at microwave or millimeter-wave frequencies.

The Wigner distribution functions of coherent and partially coherent Bessel—Gaussian beams

Abstract: Based on the integral representation of the Bessel functions and the generating function of the Tricomi function, an analytical expression of the Wigner distribution function (WDF) for a coherent or partially coherent Bessel—Gaussian beam is presented. The reduced two-dimensional WDFs are also demonstrated graphically, which reveals the dependence of the reduced WDFs on the beam parameters.

A simulation for impact of filter nonlinear phase on navigation payload

Abstract: IIR filter nonlinear phase intensifies the navigation signal distortion, performance of navigation signals would be worsened thus pseudo-code tracking accuracy is severely damaged. Namely filter group delay response impact performance of navigation signal greatly. To analyze this issue in depth, this paper established the generic model for analyzing distortion of navigation signal. In this paper, correlation loss and timing offset of S-Curve are used to assess contributions of filter phase response to payload signal. Design steerable group delay filter to precisely fit IIR filter in different group delay response aiming to minimize nonlinear phase distortion introduced by filter.

Proposal of Novel Optical Burst Signal Receiver for ONU in Optical Switched Access Network

Abstract: To realize economical optical burst signal receivers for the Optical Network Unit (ONU) of the Ethernet Optical Switched Access Network (E-OSAN), we previously implemented optical burst receivers with AC-coupling and DC-coupling using off-the-shelf components, and showed that the former offers better performance. This paper proposes a new optical burst signal receiver that uses the transfer function, Gn(s) =1-Hn(s), where Hn(s) denotes a Bessel filter transfer function of order n. We also present a method for designing the proposed receiver and clarify that it has better performance than the conventional AC-coupling one. We then present an LCR circuit synthesis of Gn(s), which is necessary to actually implement a burst receiver based on the proposal.

Approximate Closed-Form Formulas for the Zeros of the Bessel Polynomials

Abstract: We find approximate expressions and for the real and imaginary parts of the th zero of the Bessel polynomial . To obtain these closed-form formulas we use the fact that the points of well-defined curves in the complex plane are limit points of the zeros of the normalized Bessel polynomials. Thus, these zeros are first computed numerically through an implementation of the electrostatic interpretation formulas and then, a fit to the real and imaginary parts as functions of , and is obtained. It is shown that the resulting complex number is -convergent to for fixed .

A New Narrowband Phase Modulation Mathematical Identity

Abstract: A new mathematical identity is suggested to describe narrow band phase modulation and other similar physical problems instead of using the Bessel function. Bessel functions are extensively used in mathematical physics [1,2], electromagnetic wave propagation and scattering [3,4], and communication system theory [3,5,6]. Such phenomena must often be approximated by appropriate formulas since there is no closed form solution or expression, which usually leads to complex mathematical solutions [5,7]. Comparisons are made between the exact solution numerically calculated and graphed with the new mathematical identities’ prediction of phase modulation behavior. The proposed mathematical identity matches the results very well, leading to simpler analysis of such physical behavior.

A leaky radial waveguide for generating propagating Bessel beams

Abstract: We report a leaky radial waveguide that can generate propagating Bessel beams by supporting an azimuthally invariant leaky-wave mode. The normal electric-field component of the mode is a truncated, zeroth-order Bessel function. Design relations for the radial waveguide are provided based on a vector field approach in contrast to previous scalar-based approaches. Electric field measurements and their respective Fourier transforms validate the operation of the prototype as a Bessel-beam launcher. In particular, the Fourier transform of the measured electric field exhibits a ring in the spectral domain at the operating frequency, as expected for Bessel beams. The proposed structure can be used for generating arbitrary zeroth-order propagating Bessel beams at microwave or millimeter-wave frequencies.

Real-time recursive filter to identify weather events using traffic CCTV video

Abstract: A program is implemented on a processor for executing the following steps: receiving images of a scene comprising successive frames from a camera, each frame including an array of pixels; filtering intensities of the array of pixels in a respective frame by using a Bessel Filter to compute a constant value for the respective frame; and summing a predetermined number of respective frames from the camera to determine rapid motion in the scene. The filter includes a Bessel filter, which is an n-pole recursive digital filter, where n is a positive integer.

Correspondence - Design of ladder-type SAW/BAW

Abstract: This paper describes the design of RF SAW/ BAW filters with constant group delay. The band-pass LC filter is designed based on the traditional Bessel filter design. Then, LC resonators in the filter are replaced by SAW/BAW resonators with finite capacitance ratio γ. Finite γ generates passband ripples in the group delay. However, it is shown the ripples can be suppressed by optimal design of the SAW/BAW resonators. Norton's first transform is also applied to the designed filter to reduce variation of resonator shunt capacitances. Finally, extremely flat group delay with deviation of 4 ns over the frequency range of ±20 MHz at the center frequency of 1 GHz is theoretically demonstrated.

Some properties of Bessel sequences in Hilbert spaces

Abstract: Frame theory plays an important role in signal processing, image processing, data compression and sampling theory. In this short paper, some properties of Bessel sequences in Hilbert spaces are obtained, which generalize the existing results of frame to the case of Bessel sequences.

Influence of Different Packaging and Footprint Technique for Microwave Absorptive Bessel Filter's Performance

Abstract: In present day's ultra high speed data transmission environment, passive filters play a very important and critical function to achieve high-end system performance, especially in Microwave frequency ranges of 10 GHz or higher. Excellent electrical specification such as accurate −3dB cutoff frequency bandwidth, stable group delay, along with VSWR characteristics are very important parameters for system performance. Filters mechanical specification is similarly important, if not more. Products need not only be in certain size to fit in the board but also needs to be complement with other components. As available space in PCB become miniature for each component, filters footprint as well as via position need to be in certain ways to optimize board space and performance. Packaging material and packaging techniques play significant role to be ease of mass production as well. While some manufacturers like “Wirebonding” packaging, some like “Through Via”, and “Ball Grid Array” is the packaging choice of some man...

Design and application of wide-range variable fractional delay filter

Abstract: In this paper, the design and application of wide-range variable fractional delay (WVFD) is presented. First, the design of WVFD filter is studied including Lagrange method and least square (LS) method. Then, the designed WVFD filter is used to develop an adaptive sub-sample time delay estimation algorithm in which the filter coefficients are updated by using the least mean p-power (LMP) error algorithm. Finally, simulation examples are demonstrated to show the effectiveness of the proposed design and estimation method.