Title: Immittance data validation by Kramers-Kronig relations - Derivation and implications
Authors: MALKOW THOMAS
Citation: CHEMELECTROCHEM vol. 4 no. 11 p. 2777–278
Publisher: WILEY-V C H VERLAG GMBH
Publication Year: 2017
JRC N°: JRC96302
ISSN: 2196-0216
URI: http://publications.jrc.ec.europa.eu/repository/handle/JRC96302
DOI: 10.1002/celc.201700630
Type: Articles in periodicals and books
Abstract: Explicitly based on causality, linearity (superposition) and stability (time invariance) and implicit on continuity (consistency), finiteness (convergence) and uniqueness (single valuedness) in the time domain, Kramers-Kronig (KK) integral transform (KKT) relations for immittances are derived as pure mathematical constructs in the complex frequency domain using the two-sided (bilateral) Laplace integral transform (LT) reduced to the Fourier domain for sufficiently rapid exponential decaying, bounded immittances. Novel anti KK relations are also derived to distinguish LTI (linear, time invariant) systems from non-linear, unstable and acausal systems. All relations can be used to test KK transformability on the LTI principles of linearity, stability and causality of measured and model data by Fourier transform (FT) in immittance spectroscopy (IS). Also, integral transform relations are provided to estimate (conjugate) immittances at zero and infinite frequency particularly useful to normalise data and compare data. Also, important implications for IS are presented and suggestions for consistent data analysis are made which generally apply likewise to complex valued quantities in many fields of engineering and natural sciences.
JRC Directorate:Energy, Transport and Climate

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