Theory for a wavelet analysis of electrochemical noise in the laplace space with use of two operational frequencies

Abstract

The image of a random process in the Laplace space may be viewed as resulting from use of a oneway continuous wavelet transform with an exponential as the basic function, i.e. as resulting from the application of the Laplace wavelet. If the Laplace-wavelet variance of an electrochemical noise allows one to determine the Laplace transform of a time-correlation function, i.e. a factual operational spectral density of the noise, then the covariance of two Laplace waveletes of an electrochemical noise, each of which corresponds to its own operational frequency, allows one to verify a local consistency of the initial experimental noise data. The Laplace waveletes are applied rather widely. In fact, any stationary random process and stationary random time sequence can be described with operational noise spectra.