Immittance Data Validation using Fast Fourier Transformation (FFT) Computation – Synthetic and Experimental Examples

Exact data of an electric circuit (EC) model of RLC (resistor, inductor, capacitor) elements representing rational immittance of LTI (linear, time invariant) systems are numerically Fourier transformed to demonstrate within error bounds applicability of the Hilbert integral tranform (HT) and Kramers‐Kronig (KK) integral tranform (KKT) method. Immittance spectroscopy (IS) data are validated for their HT (KKT) compliance using non‐equispaced fast Fourier transformation (NFFT) computations. Failing of HT (KKT) testing may not only stem from non‐compliance with causality, stability and linearity which are readily distinguished using anti HT (KKT) relations. It could also indicate violation of uniform boundedness to be overcome either by using singly or multiply subtracted KK transform (SSKK or MSKK) or by seeking KKT of the same set of data at a complementary immit‐ tance level. Experimental IS data of a fuel cell (FC) are also numerically HT (KKT) validated by NFFT assessing whether LTI principles are met. Figures of merit are suggested to measure success in numerical validation of IS data.