ON THE TRANSFORMATION OF COLORED RANDOM NOISE BY THE KRONIG-KRAMERS INTEGRAL-TRANSFORMS

The transformation of random noise present in impedance spectroscopy d ata by the important Kronig-Kramers integral-transform relations is in vestigated analytically. It is found that the standard deviation of th e transformed noise may be smaller than the input noise under certain conditions. The output noise standard deviation depends critically on the details of the numerical quadrature procedure used for the Kronig- Kramers transformations, so the effects of several different numerical integration routines are investigated. In most cases of interest, it is proved that the standard deviation of the output noise is equal to that of the input noise, in agreement with earlier Monte Carlo results . It has been found possible not only to derive expressions for the li miting standard deviation of the transformed noise for several differe nt integration procedures but also to obtain analytic expressions for their statistical distributions in the limit of an infinite number of discrete integration points. Finally, it is demonstrated that the inte gration routine may be adjusted to obtain either very small integratio n errors (in the absence of input noise) or smaller output noise with larger integration error. (C) 1997 Elsevier Science S.A.