Haar wavelet method for the analysis of transistor circuits

Kalpana, R. A.; Balachandar, S.

doi:10.1016/j.aeue.2006.10.003

Cited by 12 publications

(5 citation statements)

References 18 publications

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“…In the wavelet analysis for a dynamic system, all functions need to be transformed into Haar series. As the differentiation of Haar wavelets always results in impulse functions which should be avoided, the integration of Haar wavelets is preferred, which should be expandable into Haar series with Haar coefficient matrix P .

\int_{0}^{t} h_{(m)} true(τ true) d τ \approx P_{true(m \times m true)} {boldh}_{true(m true)} (t), t \in [0, 1),

where the m ‐square matrix P is called the operational matrix of integration which satisfies the following recursive formula.

P_{true(m \times m true)} = \frac{1}{2 m} true[\begin{matrix} 2 m P_{true(\frac{m}{2} \times \frac{m}{2} true)} & - H_{true(\frac{m}{2} \times \frac{m}{2} true)} \\ H_{true(\frac{m}{2} \times \frac{m}{2} true)}^{- 1} & 0_{true(\frac{m}{2} \times \frac{m}{2} true)} \end{matrix} true], P_{true(1 \times 1 true)} = \frac{1}{2},

where

H_{true(m \times m true)} \overset{Δ}{=} [{boldh}_{true(m true)} true(t_{0} true) {boldh}_{true(m true)} true(t_{1...}

…”

Section: Some Properties Of Haar Waveletsmentioning

confidence: 99%

Section: Integration Of Haar Waveletsmentioning

confidence: 99%

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Numerical inversion of laplace transform via wavelet in partial differential equations

Hsiao

2013

Numerical Methods Partial

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This article presents a rational Haar wavelet operational method for solving the inverse Laplace transform problem and improves inherent errors from irrational Haar wavelet. The approach is thus straightforward, rather simple and suitable for computer programming. We define that P is the operational matrix for integration of the orthogonal Haar wavelet. Simultaneously, simplify the formulae of listing table (Chen et al., Journal of The Franklin Institute 303 (1977), 267–284) to a minimum expression and obtain the optimal operation speed. The local property of Haar wavelet is fully applied to shorten the calculation process in the task. The operational method presented in this article owns the advantages of simpler computation as well as broad application. We still can obtain satisfying solution even under large matrix. Moreover, we do not have numerically unstable problems. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 536–549, 2014

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\int_{0}^{t} h_{(m)} true(τ true) d τ \approx P_{true(m \times m true)} {boldh}_{true(m true)} (t), t \in [0, 1),

where the m ‐square matrix P is called the operational matrix of integration which satisfies the following recursive formula.

P_{true(m \times m true)} = \frac{1}{2 m} true[\begin{matrix} 2 m P_{true(\frac{m}{2} \times \frac{m}{2} true)} & - H_{true(\frac{m}{2} \times \frac{m}{2} true)} \\ H_{true(\frac{m}{2} \times \frac{m}{2} true)}^{- 1} & 0_{true(\frac{m}{2} \times \frac{m}{2} true)} \end{matrix} true], P_{true(1 \times 1 true)} = \frac{1}{2},

where

H_{true(m \times m true)} \overset{Δ}{=} [{boldh}_{true(m true)} true(t_{0} true) {boldh}_{true(m true)} true(t_{1...}

…”

Section: Some Properties Of Haar Waveletsmentioning

confidence: 99%

Section: Integration Of Haar Waveletsmentioning

confidence: 99%

Numerical inversion of laplace transform via wavelet in partial differential equations

Hsiao

2013

Numerical Methods Partial

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“…Maleknejad et al [22] suggested a rationalized Haar wavelet approach to solve a system of linear integro‐differential equations. Lepik [23] developed a segmentation method based on Haar wavelets for the solution of ODEs and PDEs, and subsequently the method has been shown to be an efficient tool for solving various kinds of linear and nonlinear problems [24, 25]. A Haar wavelet‐based method to analyze the design in the generalized state space singular system of transistor circuits was presented [26].…”

Section: Introductionmentioning

confidence: 99%

Application of the Haar wavelet method on a continuously moving convective‐radiative fin with variable thermal conductivity

Kanth

Kumar

2013

Heat Trans. Asian Res.

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In this paper, we numerically investigate the heat transfer in a continuously moving convective‐radiative fin with variable thermal conductivity by using Haar wavelets. Heat is dissipated to the environment simultaneously through convection and radiation. The effect of various significant parameters—in particular the thermal conductivity parameter a, convection‐sink temperature θa, radiation‐sink temperature θs, convection‐radiation parameter Nc, radiation‐conduction parameter Nr, and Peclet number Pe—on the temperature profile of the fin are discussed and interpreted physically through illustrative graphs. Computational results obtained by the present method are in good agreement with the standard numerical solutions. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21038

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“…[14] applies Haar wavelet based method for the analysis of observer design in the generalized state space systems of transistor circuits. It is confirmed that Haar wavelet method is better than the Walsh function techniques.…”

Section: Introductionmentioning

confidence: 99%

“…(13) in single term Haar wavelet series with (14) we obtain the following set of recursive equations with …”

Section: Introductionmentioning

confidence: 99%

Single Term Haar Wavelet Series Method for the Solution of Time Varying Singular Systems

Sekar¹,

Prabakaran

2011

2011 International Conference on Process Automation, Control and Computing

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Haar wavelet method for the analysis of transistor circuits

Cited by 12 publications

References 18 publications

Numerical inversion of laplace transform via wavelet in partial differential equations

Numerical inversion of laplace transform via wavelet in partial differential equations

Application of the Haar wavelet method on a continuously moving convective‐radiative fin with variable thermal conductivity

Single Term Haar Wavelet Series Method for the Solution of Time Varying Singular Systems

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