A modified method for circuit analysis using haar wavelet transform with adaptive resolution — For circuits with waveform with sharp convex ranges—

Oishi, Masanori; Moro, Seiichiro; Matsumoto, Tadashi

doi:10.1109/ecctd.2009.5274922

Cited by 5 publications

(6 citation statements)

References 14 publications

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“…analysis with the Haar wavelet to develop a method that begins by solving the circuit equations at a low resolution and then increases the local resolution of the solution at time instants where singular points are expected. These time instants were pre-selected by the authors [6] but it is also possible to automatically detect them [10]. Another approach [7] utilizes Chebyshev polynomials to create a biorthogonal spline wavelet basis for the steady-state analysis of power electronics circuits.…”

Section: Used Transientmentioning

confidence: 99%

“…Simulation of circuits using wavelets have been proposed for transient, steady-state, and sensitivity analysis [1]- [15]. Wavelets can potentially bring advantages in areas such as greater Jacobian matrix sparsity compared to Harmonic Balance (HB) [4], [8], a reduction in the problem size by taking advantage of the sparse representation of signals in the wavelet domain [6], [10], [11], [14], [15], and a reduction in the size of the system of equations by selecting the level of wavelets to be used during the circuit simulation [7], [9].…”

Section: Introductionmentioning

confidence: 99%

“…The approach in [11], [14] uses a Galerkin formulation which requires wavelet basis functions that can be analytically integrated and, as such, cannot be used with all wavelet families. The authors in [6], [10]…”

Section: Introductionmentioning

confidence: 99%

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Effect of Wavelet Selection on Periodic Steady-State Analysis

Fedick

Christoffersen

2020

IEEE Access

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This paper presents a study of the effect wavelet selection has on the density of the Jacobian matrix and nodal waveform coefficients of wavelet based periodic steady-state analysis of electrical circuits. For the presented case studies, it is shown that a simulation in the time domain produces a sparser Jacobian matrix than a simulation in the wavelet domain if no frequency domain elements are present. When frequency domain elements are present, some wavelets may produce marginally lower densities than the time domain with the advantage of a sparser representation of the circuit waveforms. Additionally, a new method for automatically selecting the threshold used when removing low amplitude elements in the Jacobian matrix at each iteration is introduced and tested. INDEX TERMS Adaptive Jacobian thresholding, circuit simulation, Newton-Raphson method, steady-state analysis, wavelets.

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Section: Used Transientmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effect of Wavelet Selection on Periodic Steady-State Analysis

Fedick

Christoffersen

2020

IEEE Access

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“…The selective filtering method proposed here designs a wavelet family that decomposes the signal to be filtered into sub-bands fitted in amplitude, obtaining good quantitative results in terms of accuracy of filtering and simultaneously with a low computational cost. Although this technique has been studied in several digital signal processing applications, so far it has not been widely explored in digital circuit theory [13][14][15], which is the main focus of this investigation, primarily the digital filter synthesis, showing the good choice for wavelets in digital filtering applications.…”

Section: Introductionmentioning

confidence: 99%

Designing digital filter banks using wavelets

Penedo

Netto

Justo

2019

EURASIP J. Adv. Signal Process.

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In digital filters theory, filtering techniques generally deal with pole-zero structures. In this context, filtering schemes, such as infinite impulse response (IIR) filters, are described by linear differential equations or linear transformations, in which the impulse response of each filter provides its complete characterization, under filter design specifications. On the other hand, finite impulse response (FIR) digital filters are more flexible than the analog ones, yielding higher quality factors. Since many approaches to the circuit synthesis using the wavelet transform have been recently proposed, here we present a digital filter design algorithm, based on signal wavelet decomposition, which explores the energy partitioning among frequency sub-bands. Exploring such motivation, the method involves the design of a perfect reconstruction wavelet filter bank, of a suitable choice of roots in the Z-plane, through a spectral factorization, exploring the orthogonality and localization property of the wavelet functions. This approach resulted in an energy partitioning across scales of the wavelet transform that enabled a superior filtering performance, in terms of its behavior on the pass and stop bands. This algorithm presented superior results when compared to windowed FIR digital filter design, in terms of the intended behavior in its transition band. Simulations of the filter impulse response for the proposed method are presented, displaying the good behavior of the method with respect to the transition bandwidth of the involved filters.

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“…Recursive formulations of various operational matrices, derived by Hsiao et al, have been applied invariably for different applications in the literature until now [11][12][13]. However, these recursive formulations are computationally expensive.…”

mentioning

confidence: 98%

Non-recursive Haar Connection Coefficients Based Approach for Linear Optimal Control

Garg

Dewan

2011

J Optim Theory Appl

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In the present paper, two-fold contributions are made. First, non-recursive formulations of various Haar operational matrices, such as Haar connection coefficients matrix, backward integral matrix, and product matrix are developed. These non-recursive formulations result in computationally efficient algorithms, with respect to execution time and stack-and-memory overflows in computer implementations, as compared to corresponding recursive formulations. This is demonstrated with the help of MATLAB PROFILER. Later, a unified method is proposed, based on these non-recursive connection coefficients, for solving linear optimal control problems of all types, irrespective of order and nature of the system. This means that the single method is capable of optimizing both time-invariant and time-varying linear systems of any order efficiently; it has not been reported in the literature so far. The proposed method is applied to solve finite horizon LQR problems with final state control. Computational efficiency of the proposed method is established with the help of comparison on computation-time at different resolutions by taking several illustrative examples.

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A modified method for circuit analysis using haar wavelet transform with adaptive resolution — For circuits with waveform with sharp convex ranges—

Cited by 5 publications

References 14 publications

Effect of Wavelet Selection on Periodic Steady-State Analysis

Effect of Wavelet Selection on Periodic Steady-State Analysis

Designing digital filter banks using wavelets

Non-recursive Haar Connection Coefficients Based Approach for Linear Optimal Control

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