SPECTROSCOPY APPLICATIONS OF THE KRAMERS-KRONIG TRANSFORMS - IMPLICATIONS FOR ERROR STRUCTURE IDENTIFICATION

Stochastic errors were found to propagate through the Kramers-Kronig r elations in such a manner that the respective standard deivations of t he real and imaginary components of complex quantities at any given fr equency are equal. The only requirements were that the errors be stati onary in the sense of replication at each measurement frequency, that errors be uncorrelated with respect to frequency, that the derivative of the variance with respect to frequency exists, and that the Kramers -Kronig relations be satisfied. Experimental results for elecrochemica l and rheological systems are presented which support the conclusion t hat the real and imaginary components have the same variance. This res ult and the conclusions reported herein appear to be general and shoul d apply for any physical system in which the real and imaginary compon ents are obtained from the same measurement.