Frequency Analysis of Transients in Electrochemical Noise: Mathematical Relationships and Computer Simulations

The relationship between electrochemical noise (EN) time records and the power spectral densities (PSD) derived from them was examined. It was shown how the PSD of EN consisting of a series of transients depends upon the shape and statistical time distribution of the transients, as well as the distribution function of their characteristic parameters, such as amplitude or lifetime, when they show a random behavior. In particular, it was shown, analytically and by computer simulations, that the PSD exhibit negative slopes in even powers of the frequency, which depend upon the existence of singularities in the functions describing the transients. The presence of lobes and oscillations was explained by the existence of regularly spaced features in the transients. Examination of the PSD allowed the extraction of some characteristics of the EN transients that gave information on the physical processes causing them, even when the transients were superimposed in such a way as to be indistinguishable individually.