Search results for "Spline"
showing 10 items of 170 documents
Wavelet-based efficient simulation of electromagnetic transients in a lightning protection system
2003
In this paper, a wavelet-based efficient simulation of electromagnetic transients in a lightning protection systems (LPS) is presented. The analysis of electromagnetic transients is carried out by employing the thin-wire electric field integral equation in frequency domain. In order to easily handle the boundary conditions of the integral equation, semiorthogonal compactly supported spline wavelets, constructed for the bounded interval [0,1], have been taken into account in expanding the unknown longitudinal currents. The integral equation is then solved by means of the Galerkin method. As a preprocessing stage, a discrete wavelet transform is used in order to efficiently compress the Fouri…
Discrete Periodic Spline Wavelets and Wavelet Packets
2014
Similarly to periodic polynomial splines, existence of the set of embedded discrete periodic splines spaces \(\varPi [N]= \fancyscript{S}_{[0]}\supset {}^{2r} \fancyscript{S}_{[1]}\supset \cdots \supset {}^{2r} \fancyscript{S}_{[m]}\cdots \), combined with the DSHA provides flexible tools for design and implementation of wavelet and wavelet packet transforms. As in the polynomial case, all the calculations consist of fast direct and inverse Fourier transforms (FFT and IFFT, respectively) and simple arithmetic operations. Raising the splines order does not increase the computation complexity.
Biorthogonal Wavelet Transforms
2015
Wavelets in the polynomial and discrete spline spaces were introduced in Chaps. 8 and 10, respectively. In both cases, the wavelets’ design and implementation of the transforms were associated with perfect reconstruction (PR) filter banks. In this chapter, those associations are discussed in more detail. Biorthogonal wavelet bases generated by PR filter banks are investigated and a few examples of compactly supported biorthogonal wavelets are presented. Conditions for filters to restore and annihilate sampled polynomials are established (discrete vanishing moment property). In a sense, the material of this chapter is introductory to Chap. 12, where splines are used as a source for (non-spli…
Periodic Spline Wavelets and Wavelet Packets
2014
This chapter presents wavelets and wavelet packets in the spaces of periodic splines of arbitrary order, which, in essence, are the multiple generators for these spaces. The SHA technique provides explicit representation of the wavelets and wavelet packets and fast implementation of the transforms in one and several dimensions.
Optimal Control Under Fuzzy Conditions for Dynamical Systems Associated with the Second Order Linear Differential Equations
2020
This paper is devoted to an optimal trajectory planning problem with uncertainty in location conditions considered as a problem of constrained optimal control for dynamical systems. Fuzzy numbers are used to incorporate uncertainty of constraints into the classical setting of the problem under consideration. The proposed approach applied to dynamical systems associated with the second order linear differential equations allows to find an optimal control law at each \(\alpha \)-level using spline-based methods developed in the framework of the theory of splines in convex sets. The solution technique is illustrated by numerical examples.
Nonlinear impact estimation in spatial autoregressive models
2018
International audience; This paper extends the literature on the calculation and interpretation of impacts for spatial autoregressive models. Using a Bayesian framework, we show how the individual direct and indirect impacts associated with an exogenous variable introduced in a nonlinear way in such models can be computed, theoretically and empirically. Rather than averaging the individual impacts, we suggest to graphically analyze them along with their confidence intervals calculated from Markov chain Monte Carlo (MCMC). We also explicitly derive the form of the gap between individual impacts in the spatial autoregressive model and the corresponding model without a spatial lag and show, in…
An Advanced Numerical Model in Solving Thin-Wire Integral Equations by Using Semi-Orthogonal Compactly Supported Spline Wavelets
2003
Abstract—In this paper, the semi-orthogonal compactly sup- ported spline wavelets are used as basis functions for the efficient solution of the thin-wire electric field integral equation (EFIE) in frequency domain. The method of moments (MoM) is used via the Galerkin procedure. Conventional MoM directly applied to the EFIE, leads to dense matrix which often becomes computation- ally intractable when large-scale problems are approached. To overcome these difficulties, wavelets can be used as a basis set so obtaining the generation of a sparse matrix; this is due to the local supports and the vanishing moments properties of the wavelets. In the paper, this technique is applied to analyze elec…
Эмануэль Гринберг - выдающиеся достижения в прикладной математике: радио-фильтры, корпуса танкеров, графы и интегральные схемы Emanuels Grinbergs - i…
2018
The paper is dedicated to the 50th anniversary of the Grinberg theorem. The main works of Emanuel Grinberg (1911-1982) in applied mathematics are described, following the stages of his life path, namely: the design of radio receivers and the calculation of radio filters (1949-1959), hull of tanker calculations (1962-1964), the study of graph theory and the proof of the Grinberg theorem (1968), designing of integrated circuits (1968-1980). Calculations of radio filters are associated with the expansion of the use of continued fractions for the analysis of linear electric circuits (the Kauer model) and the developing of new tools – the Grinberg brackets (as an extension of the Euler brackets)…
Simulation of a single-phase five-level cascaded H-Bridge inverter with multicarrier SPWM B-Spline based modulation techniques
2017
Multilevel Power Inverters are now often used to convert DC to AC voltage waveform. This kind of converter allows high power quality with low output harmonics and lower commutation losses with respect to the traditional ones in order to optimize this aspect. This paper presents a novel simulation analysis of the Multicarrier Sinusoidal Pulse Width Modulation (MC SPWM) techniques B-Spline functions based to control the switches of five-level single-phase cascaded H-bridge inverter. In order to verify the performance of the converter, the harmonic content of the voltage due to modulation techniques has been taken into account. Results highlight the comparison between different B-Spline functi…
Baseband predistorter using direct spline computation
2005
A baseband predistorter is presented. Key features of the predistorter reside in the use of cubic spline interpolation to generate predistorted input data to the power amplifier, without time convergence problems of classical approaches, with the goal of a reduction in the computational effort. Simulated behaviour of the proposed scheme is presented, demonstrating the effectiveness of the approach.