Spectroscopy Applications of the Kramers‐Kronig Transforms: Implications for Error Structure Identification

Abstract

Stochastic errors were found to propagate through the Kramers-Kronig relations in such a manner that the respective standard deivations of the real and imaginary components of complex quantities at any given frequency are equal. The only requirements were that the errors be stationary 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 elecrochemical and rheological systems are presented which support the conclusion that the real and imaginary components have the same variance. This result and the conclusions reported herein appear to be general and should apply for any physical system in which the real and imaginary components are obtained from the same measurement.) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 192.236.36.29

Electrochemical Impedance Spectroscopy and its Applications

“…An example of such an analysis is presented in Exercise 14.1. Several examples are discussed in the literature [613,624,[627][628][629][630][631][632].…”

A Bayesian view on the Hilbert transform and the Kramers-Kronig transform of electrochemical impedance data: Probabilistic estimates and quality scores

“…The DRT-only part of the EIS spectrum, i.e., DRT , for which the resistance and inductance contributions are not considered, can be obtained at ⋆ using DRT ( ⋆ ) = DRT (27) where the DRT ∈ ℝ ×( +1) is defined following an analogous reasoning and notation behind (23) and (26). In particular, we will define the entries of DRT,re or DRT,im to be 0 in the first column, i.e.…”

“…While the exact implementation of KK relations needs impedance data for all possible frequencies, the EIS spectra, in reality, are only discretely sampled over a finite interval of frequencies. Methods, including direct integration and regression of generalized circuit models, [18,[23][24][25][26][27][28][29][30] have been developed to overcome this limitation. Consequently, the KK relations have been available as a tool to assess the validity of the EIS spectra.…”

The Gaussian Process Hilbert Transform (GP-HT): Testing the Consistency of Electrochemical Impedance Spectroscopy Data

“…One could find out how such models affect the GP-HT prediction or, conversely, if the GP-HT can be used to obtain experimental errors. 31,67 To that end, the analysis of both artificial and real experiments is needed.…”