Theory of the wavelet analysis for electrochemical noise by use of Laguerre functions

Boris M. Grafov, Irina Grafova

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

It is shown that the wavelet transform that uses the Laguerre function as a basis function is a useful tool to analyse the stationary electrochemical noise. Knowledge of the variance of the Laguerre wavelet of noise allows the Laplace transform of the correlation function to be found. The Laplace transform of the correlation function may be referred to the spectral density in the Laplace domain as well as to the operational spectral density of noise. It is shown that the operational spectral density of noise can be found not only by averaging over the ensemble of realizations of the noise process but also by averaging over the ensemble of Laguerre wavelets. The results obtained can be useful not only for analysis of electrochemical noise but also for analysis of any stationary random process, in particular for the time series analysis in econometric research. (C) 2000 Elsevier Science S.A.

Original languageEnglish (US)
Pages (from-to)386-389
Number of pages4
JournalElectrochemistry Communications
Volume2
Issue number6
DOIs
StatePublished - Oct 4 2000

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Wavelet analysis
Spectral density
Laplace transforms
Time series analysis
Random processes
Wavelet transforms

All Science Journal Classification (ASJC) codes

  • Electrochemistry

Cite this

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Theory of the wavelet analysis for electrochemical noise by use of Laguerre functions. / Grafov, Boris M.; Grafova, Irina.

In: Electrochemistry Communications, Vol. 2, No. 6, 04.10.2000, p. 386-389.

Research output: Contribution to journalArticle

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AB - It is shown that the wavelet transform that uses the Laguerre function as a basis function is a useful tool to analyse the stationary electrochemical noise. Knowledge of the variance of the Laguerre wavelet of noise allows the Laplace transform of the correlation function to be found. The Laplace transform of the correlation function may be referred to the spectral density in the Laplace domain as well as to the operational spectral density of noise. It is shown that the operational spectral density of noise can be found not only by averaging over the ensemble of realizations of the noise process but also by averaging over the ensemble of Laguerre wavelets. The results obtained can be useful not only for analysis of electrochemical noise but also for analysis of any stationary random process, in particular for the time series analysis in econometric research. (C) 2000 Elsevier Science S.A.

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