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Showing papers on "Bessel filter published in 2017"


Journal ArticleDOI
TL;DR: In this article, the Bessel filter is applied to a spectral-element-based elastic full waveform inversion framework, and the associated linear system is solved efficiently through a parallel conjugate gradient algorithm, in which the matrix vector product is factorized and highly optimized with vectorized computation.
Abstract: Smoothing filters are extremely important tools in seismic imaging and inversion, such as for traveltime tomography, migration and waveform inversion. For efficiency, and as they can be used a number of times during inversion, it is important that these filters can easily incorporate prior information on the geological structure of the investigated medium, through variable coherent lengths and orientation. In this study, we promote the use of the Bessel filter to achieve these purposes. Instead of considering the direct application of the filter, we demonstrate that we can rely on the equation associated with its inverse filter, which amounts to the solution of an elliptic partial differential equation. This enhances the efficiency of the filter application, and also its flexibility. We apply this strategy within a spectral-element-based elastic full waveform inversion framework. Taking advantage of this formulation, we apply the Bessel filter by solving the associated partial differential equation directly on the spectral-element mesh through the standard weak formulation. This avoids cumbersome projection operators between the spectral-element mesh and a regular Cartesian grid, or expensive explicit windowed convolution on the finite-element mesh, which is often used for applying smoothing operators. The associated linear system is solved efficiently through a parallel conjugate gradient algorithm, in which the matrix vector product is factorized and highly optimized with vectorized computation. Significant scaling behaviour is obtained when comparing this strategy with the explicit convolution method. The theoretical numerical complexity of this approach increases linearly with the coherent length, whereas a sublinear relationship is observed practically. Numerical illustrations are provided here for schematic examples, and for a more realistic elastic full waveform inversion gradient smoothing on the SEAM II benchmark model. These examples illustrate well the efficiency and flexibility of the approach proposed.

33 citations


Journal ArticleDOI
TL;DR: In this paper, the radius of uniform convexity for three kinds of normalized Bessel functions of the first kind was determined and necessary and sufficient conditions were given for the parameters of the three normalized functions such that they were uniformly convex in the open unit disk.

31 citations


Journal ArticleDOI
TL;DR: In this paper, the simulation design and performance analysis of RZ-OOK VLC system under the influence of optical background noise using optisystem software is proposed, where Rectangular optical filter, placed before the photo-diode and electrical low pass Bessel filter after the trans-impedance amplifier are used to mitigate the noise.

23 citations


Journal ArticleDOI
TL;DR: An exact solution of expansion coefficients for a T-matrix method interacting with acoustic scattering of arbitrary order Bessel beams from an obstacle of arbitrary location is derived analytically.
Abstract: An exact solution of expansion coefficients for a T-matrix method interacting with acoustic scattering of arbitrary order Bessel beams from an obstacle of arbitrary location is derived analytically. Because of the failure of the addition theorem for spherical harmonics for expansion coefficients of helicoidal Bessel beams, an addition theorem for cylindrical Bessel functions is introduced. Meanwhile, an analytical expression for the integral of products including Bessel and associated Legendre functions is applied to eliminate the integration over the polar angle. Note that this multipole expansion may also benefit other scattering methods and expansions of incident waves, for instance, partial-wave series solutions.

21 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered the problem of detecting the true dimension of a Brownian particle in a two-dimensional plane or in a three-dimensional space, given that only the distance of the particle to the origin is being observed.
Abstract: Consider the motion of a Brownian particle that takes place either in a twodimensional plane or in the three-dimensional space. Given that only the distance of the particle to the origin is being observed, the problem is to detect the true dimension as soon as possible and with minimal probabilities of the wrong terminal decisions. We solve this problem in the Bayesian formulation under any prior probability of the true dimension when the passage of time is penalised linearly.

19 citations


Proceedings ArticleDOI
TL;DR: In this article, a 2D raster scanning quasi-static/resonant micro mirror was controlled in both axes in closed-loop with on-chip piezo-resistive sensor feedback.
Abstract: In this paper we present a 2D raster scanning quasi-static/resonant micro mirror being controlled in both axes in closed-loop with on-chip piezo-resistive sensor feedback. While the resonant axis oscillates with a given frequency, the quasi-static axis allows static as well as dynamic deflection up to its eigenfrequency because of its staggered vertical comb (SVC) drive arrangement. Due to the high quality factor of the very low damped spring-masssystem, an adapted trajectory planning using jerk limitation is applied for the quasi-static axis [1]. Nevertheless, inaccuracies of the applied nonlinear micro mirror model and external disturbances lead to undesired residual oscillation in open-loop control mode. To achieve high precise and fast beam positioning, we implement a flatness-based control algorithm with feedback to on-chip piezo-resistive deflection sensors. In comparison to previous work [2, 3], we developed a micro controller setup for driving the microscanner, that is equipped with an analog Bessel filter increasing the sensor signal quality significantly. In this study we demonstrate a small size and low power micro mirror driver including high-voltage generation and a microcontroller for real-time control as well as a head circuit board for high resolution sensing. We discuss experimental results of open-loop and closed-loop control for 2D raster scanning operation. Finally, the outlook is given to the intrinsic capability to compensate temperature drifts influencing the piezo-resistive sensor signal.

18 citations


Journal ArticleDOI
TL;DR: Multi-resolution quadrature rules based on hybrid functions and Haar wavelets are used as supporting tools to handle the case of singularity of the meshless collocation method.

17 citations


Journal ArticleDOI
TL;DR: In this paper, a phase-only spatial light modulator (SLM) and an iterative Fourier transformation algorithm (IFTA) are used to create an annular light distribution in the back focal plane of a lens.

10 citations


Journal ArticleDOI
TL;DR: In this paper, two new classes of generalized-tempered Bessel functions on a compact domain [0,T] are presented, which are denoted by GTBFs-1 and GTBF-2.
Abstract: This paper presents 2 new classes of the Bessel functions on a compact domain [0,T] as generalized-tempered Bessel functions of the first- and second-kind which are denoted by GTBFs-1 and GTBFs-2. Two special cases corresponding to the GTBFs-1 and GTBFs-2 are considered. We first prove that these functions are as the solutions of 2 linear differential operators and then show that these operators are self-adjoint on suitable domains. Some interesting properties of these sets of functions such as orthogonality, completeness, fractional derivatives and integrals, recursive relations, asymptotic formulas, and so on are proved in detail. Finally, these functions are performed to approximate some functions and also to solve 3 practical differential equations of fractionalorders.

9 citations


Proceedings ArticleDOI
01 Nov 2017
TL;DR: In this article, the authors investigated the mass change process in a Rogowski coil transformer (differential, filtering, sampling, and integration) and analyzed the mechanism of the abnormal waveform generated in the transformer.
Abstract: The Rogowski coil current transformer is typically influenced by the high-frequency transient current generated during switching operations or short-circuit fault. This paper investigated the mass change process in a Rogowski coil transformer (differential, filtering, sampling, and integration) and analyzed the mechanism of the abnormal waveform generated in the transformer. Results showed that appropriate configuration of a low-pass filter placed before the collector reduced the amplitude of the high frequency component in the signal, resulting in attenuated amplitude of frequency components after aliasing. The filter also inhibited abnormal waveforms by increasing the sampling frequency of the sampler. Simulation results showed that the use of a fourth-order Bessel filter to suppress high frequency signals and increase sampling rate to 100kHz is feasible and effective. The approach proposed in this study is shown to improve the operational reliability of Rogowski coil transformers.

9 citations


Journal ArticleDOI
TL;DR: Some new properties of the modulus and phase functions and some asymptotic expansions derived from differential equation theory are given and a bound on the error of the first term of this asymPTotic expansion is found.
Abstract: The Bessel phase functions are used to represent the Bessel functions as a positive modulus and an oscillating trigonometric term. This decomposition can be used to aid root-finding of certain combinations of Bessel functions. In this article, we give some new properties of the modulus and phase functions and some asymptotic expansions derived from differential equation theory. We find a bound on the error of the first term of this asymptotic expansion and give a simple numerical method for refining this approximation via standard routines for the Bessel functions. We then show an application of the phase functions to the root finding problem for linear and cross-product combinations of Bessel functions. This method improves upon previous methods and allows the roots in ascending order of these functions to be calculated independently. We give some proofs of correctness and global convergence.


Journal ArticleDOI
TL;DR: In this article, an efficient, spatially variant correlation filter for anisotropic dip filtering is proposed, based on the Laplace correlation function, for which there exists analytical expressions for the correlation kernel and its inverse kernel in the 1D case.
Abstract: We have developed a computational framework that allows an efficient, spatially variant correlation filter for anisotropic dip filtering. The approach is based on the Laplace correlation function, for which there exists analytical expressions for the correlation kernel and its inverse kernel in the 1D case. An extension to higher dimensions by adding orthogonal 1D inverse functions provides a linear equation whose solution is identical to applying a Bessel filter. We have found that a good approximation of the Laplace filter function is obtained by applying a cascade of Bessel filters. We implement such an inverse operator on regular grids with a finite-difference stencil, giving a sparse matrix for the linear equation, which can be solved efficiently through a conjugate-gradient algorithm. Computing such a correlation operation by solving the linear system involving the inverse operator is significantly faster than applying the correlation function via convolution or windowed convolution: Solving...

Proceedings ArticleDOI
09 Jun 2017-Rice
TL;DR: This research work brings operational transresistance amplifier (OTRA) based second order universal filter, with three main filter optimizations like Butterworth, Chebyshev and Bessel, based on the RC-RC decomposition technique.
Abstract: This research work brings operational transresistance amplifier (OTRA) based second order universal filter, with three main filter optimizations like Butterworth, Chebyshev and Bessel. The universal filter offers all five sections of filter responses likes: Low-Pass, High-Pass, Band-Pass, BandRejection and All-Pass. Design is based on the RC-RC decomposition technique. Finally, simulation results are performed to verify the theoretical results using ORCAD 10.5 circuit simulator.

Patent
22 Mar 2017
TL;DR: In this article, a satellite-borne laser range finder echo detection circuit is described, and the circuit comprises a power filtering circuit, an APD detector (module), a differential amplifier circuit, a passive Bessel filter circuit, and a transformer isolation circuit.
Abstract: The invention discloses a satellite-borne laser range finder echo detection circuit, and the circuit comprises a power filtering circuit, an APD detector (module), a differential amplifier circuit, a passive Bessel filter circuit, and a transformer isolation circuit. The power filtering circuit carries out the filtering of an input power supply, so as to meet the requirements of each unit of the detection circuit for power ripples and noise. The APD detector (module) is a photoelectric device which achieves the laser echo detection, obtains an internal gain under the condition of external high-voltage bias, and achieves the detection of a weak signal. The differential amplifier circuit is used for converting a single-end current (voltage) signal outputted by the APD detector (module) into a differential signal, and improves the anti-interference capability of signal transmission. The passive Bessel filter circuit enables the signal bandwidth to be limited in a proper frequency band range under the condition of guaranteeing no signal distortion, so as to obtain the optimal SNR and meet the demands of different applications.

Proceedings ArticleDOI
07 Mar 2017
TL;DR: A comprehensive fitness function for IIR digital filter design with 6 terms is proposed, including a new term to get a filter with low delay to show lower delay of designed filters by proposed method than designed ones by traditional methods.
Abstract: Digital IIR filter design by optimizing a fitness function with respect to coefficients of a filter with rational transfer function by meta-heuristic algorithms has been considered recently. Most researchers use a fitness function consisted of difference between magnitude response of desired filter and designed filter and the constraints such as linear phase, minimum phase and stability of designed filter. In this paper, a comprehensive fitness function for IIR digital filter design with 6 terms is proposed. A new term is added to fitness function to get a filter with low delay. Low delay filters are desirable for real time signal processing. This term is weighted partial energy of the impulse response of designed causal filter. Maximizing this term leads to concentration of energy of impulse response at its beginning, consequently a low delay filter. Low delay property leads to fast decaying of transient response and low delay between input and output of designed filter. Proposed fitness function also includes some terms to meet linear phase, minimum phase and stability constraints. Meta-heuristic optimization algorithms GA, GSA and PSO are used to optimize proposed fitness function. To evaluate efficiency of the proposed method, it will be used to design a low delay low pass filter and a low delay differentiator. Reported results show lower delay of designed filters by proposed method than designed ones by traditional methods.

Journal ArticleDOI
TL;DR: In this paper, a simple uniform bound for the ratio of two modified spherical Bessel functions is derived, where the arguments of the two functions are complex, but their ratio is real.

Patent
20 Jul 2017
TL;DR: In this article, a signal output device is provided in a communication apparatus and the signal output unit outputs a signal which is obtained by passing a predetermined signal through the first filter and the second filter.
Abstract: A signal output device is provided in a communication apparatus The communication apparatus communicates with a different one of the communication apparatus using a single line The signal output device includes a signal output unit The signal output unit includes a first filter and a second filter The first filter is provided by a Bessel filter The second filter is provided by a Chebyshev filter or a Butterworth filter The signal output unit outputs a signal which is obtained by passing a predetermined signal through the first filter and the second filter The signal output from the signal output unit has a pass characteristic of the first filter and a pass characteristic of the second filter A cutoff frequency of the first filter is set to be lower than a cutoff frequency of the second filter

Proceedings ArticleDOI
01 Jun 2017
TL;DR: A continued fraction expansion different from that in the Bessel filter brings a novel analog FIR filter that is composed of only passive elements and provides wideband signal processing.
Abstract: A continued fraction expansion different from that in the Bessel filter brings a novel analog FIR filter. The circuit block including a delay component is composed of only passive elements and provides wideband signal processing. Element values are explicitly expressed without a parameter of the degree of approximation. This building block is utilized in FIR filter design together with transconductors. Design example shows that the proposed scheme reduces the circuit area.


Patent
22 Dec 2017
TL;DR: In this article, the authors proposed an electronic transformer integration method in GIS using the Rogowski coil principle in a low-pass filtered Bessel filter and an FPGA in the remote module of the electronic transformer.
Abstract: The invention relates to an electronic transformer integration method in GIS The method comprises the steps that (1) after a signal output from the sensor element of an electronic transformer is low-pass filtered by a fourth-order Bessel filter, a high-precision analog-digital conversion device carries out high-rate sampling in a timing manner; and (2) an integral algorithm is completed by an FPGA, wherein the FPGA is placed in the remote module of the electronic transformer According to the invention, the fourth-order Bessel filter is used; the A/D sampling rate is improved to 100kHz; the passage of high-frequency signals is suppressed through hard-soft combination; software integration is completed by the FPGA in the remote module; other improvement measures are adopted; the experiment proves that the proposal of the invention is feasible and helps to improve the operational reliability of the electronic transformer using the Rogowski coil principle in GIS

Proceedings ArticleDOI
12 Jun 2017
TL;DR: In this article, a novel smoothing strategy based on the Bessel filter is proposed, which is performed by solving the elliptic partial differential equation associated to its sparse inverse operator, in which the matrix-vector product is factorized and optimized in a similar way as the one used for solving the elastodynamic system.
Abstract: Summary Smoothing filters are extremely important tools in seismic imaging and especially in full waveform inversion. For complex geological structures with variable heterogeneities, these filters should be able to incorporate efficiently geological prior information of the target medium, through coherent lengths and 3D orientation, which are expected to vary in space. In this study, we introduce a novel smoothing strategy based on the Bessel filter, for which we are able to design a highly efficient implementation. Its application is performed by solving the elliptic partial differential equation associated to its sparse inverse operator. The development of this equation in any discretization method naturally yields a symmetric and well-conditioned linear system. We develop this smoothing strategy within an elastic spectral-element-based full-waveform-inversion framework. The associated linear system can be solved efficiently through a parallel conjugate-gradient algorithm, in which the matrix-vector product is factorized and optimized in a similar way as the one used for solving the elastodynamic system. By doing so, we avoid expensive explicit-windowed-convolution over the finite element mesh. The efficiency and the flexibility of the proposed smoothing method are illustrated through various schematic examples, and on a more realistic elastic full waveform inversion problem on the SEAM II benchmark model.

Proceedings ArticleDOI
01 Oct 2017
TL;DR: The design solutions and performance of these two electronic apparatus are presented: the stabilization system for the COSINUS detector and the prototype signal filtering and digitization system.
Abstract: The COSINUS collaboration aims to develop a cryogenic scintillating calorimeter for the search of dark matter, using undoped sodium iodide crystals as target. The simultaneous measurement of the phonon and light signal - both read out by Transition Edge Sensors (TESs) - allows to discriminate between signal and background events. For proper functioning, TESs have to operate close to their characteristic transition temperature, hence there is the need for a programmable, very stable and high resolution working point stabilization and biasing system. For this purpose, we designed a flexible 2-channel custom board, which is able to generate a programmable current with a 12-bit resolution. Current full-scale ranges can be further selected with 5 bits, for better flexibility during detector characterization. Each channel can be used for both TES biasing and TES temperature stabilization via a dedicated heater. The same board is also able to inject custom-shaped current pulses into the heater, in order to periodically calibrate the energy response of the detector and to calibrate the TES transition point. The thermal drifts are compensated using an 8-bit trimmer, reaching a stability over temperature of less than 1 ppm$/ ^{circ}\mathrm{C}$. The board is based on a Cortex-M3 microcontroller and is remotely controlled through an optically connected CAN bus. We also designed a prototypal signal filtering and digitization board, which consist of a 12-channel 6-pole Bessel filter with programmable cut-off frequencies between 24 Hz and 2.4 kHz. An onboard 50 ksps ADC with an effective RMS resolution of 20.2 bits is responsible of the signal digitization. In this contribution, we present the design solutions and performance of these two electronic apparatus: the stabilization system for the COSINUS detector and the prototype signal filtering and digitization system.

Journal ArticleDOI
TL;DR: In this article, a set of frame generators for a unitary system which is closed under linear combinations is introduced, and several sufficient conditions such that an operator is a frame generator multiplier for certain unitary systems are given.
Abstract: In this paper, we introduce a set of frame generators for a unitary system which is closed under linear combinations. Certain structural properties of the set are studied. Then we give several sufficient conditions such that an operator is a frame generator multiplier for certain unitary systems. Since there are two natural norms endowed with each Bessel multiplier, i.e., the usual operator norm and the Bessel norm, we compare these norms of Bessel multipliers for some cases.

Proceedings ArticleDOI
01 Dec 2017
TL;DR: The paper analyzes the influence of the Bessel filter frequency characteristics on the efficiency of the DCT trigger.
Abstract: The standard triggers T1 and ToT for the surface detectors of the Pierre Auger Observatory based on 3-fold (T1) or 2-fold (ToT) coincidences in the time domain The Discrete Cosine Transform (DCT) algorithm implemented as 3 engines for 3 PMT channels implemented into the surface detector Front-End Board (FEB) FPGA analyzes online shapes of the signal waveforms (ADC traces) and generates a trigger if selected number (7–9) of sub-triggers (as scaled DCT[k]/DCT[1]) are “fired” in at least two channels simultaneously For assumed sampling frequency f S = 120 MHz, the filter is built from RLC components on relatively small values Resistors and inductors are available in 01 % and 5 % tolerance, however, capacitors in pF range are available even in 01 pF, but the parasitic capacitance on the FEB can dramatically change the frequency characteristics Daily temperature variations reach even 40 ° C, which additionally change the characteristic of the analog FEB section The paper analyzes the influence of the Bessel filter frequency characteristics on the efficiency of the DCT trigger

Journal ArticleDOI
TL;DR: In this article, the authors proposed a novel generation method for Rayleigh distribution clutter in CR, which adopts white Gaussian noise sequence and Bessel filter, and can be generated through nonlinear transformation.
Abstract: Research on clutter modeling and generation is very important in echo analysis, especially for CR (cognitive radar) working in complex environment. In this paper, we propose a novel generation method for Rayleigh distribution clutter in CR. This method adopts white Gaussian noise sequence and Bessel filter, and Rayleigh distribution clutter can be generated through nonlinear transformation. Simulation results demonstrate the validity of the method, and the estimated value and theoretical value are consistent with each other in both clutter amplitude and spectrum. Finally, the whole paper is summarized.