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

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.