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Summary
This summary is machine-generated.

This study validates the Kramers-Kronig (KK) transform for electric circuit models using immittance spectroscopy data. It demonstrates the KK transform

Keywords:
Boundednesscausalitycontinuitylinearitystability

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Area of Science:

  • Electrical Engineering and Applied Physics
  • Physical Chemistry and Materials Science

Background:

  • Linear, time-invariant (LTI) systems are fundamental in electrical engineering and physical sciences.
  • The Kramers-Kronig (KK) transform is a powerful tool for validating causality and physical realizability of system responses.
  • Immittance spectroscopy (IS) provides frequency-dependent electrical response data crucial for material characterization.

Purpose of the Study:

  • To numerically validate the applicability of the Hilbert transform (HT) and Kramers-Kronig (KK) integral transform (KKT) method for rational immittance data of RLC circuits.
  • To assess the compliance of immittance spectroscopy (IS) data with HT (KKT) relations using non-equispaced fast Fourier transformation (NFFT).
  • To investigate potential reasons for HT (KKT) test failures beyond non-compliance with causality, stability, and linearity, including uniform boundedness violations.

Main Methods:

  • Numerical Fourier transformation of exact electric circuit (EC) model data for RLC elements.
  • Validation of immittance spectroscopy (IS) data using non-equispaced fast Fourier transformation (NFFT) for Hilbert transform (HT) and Kramers-Kronig (KK) compliance.
  • Application of anti-HT (anti-KKT) relations to distinguish causality, stability, and linearity violations.
  • Exploration of singly or multiply subtracted KK transforms (SSKK or MSKK) for uniform boundedness issues.
  • Numerical HT (KKT) validation of experimental IS data from a fuel cell (FC) using NFFT.

Main Results:

  • Demonstrated the applicability of the Hilbert transform (HT) and Kramers-Kronig (KK) integral transform (KKT) method for RLC circuit immittance data within error bounds.
  • Validated experimental IS data from a fuel cell (FC) using NFFT to confirm adherence to LTI principles.
  • Identified that HT (KKT) test failures can arise from violations of uniform boundedness, not solely causality, stability, or linearity.

Conclusions:

  • The Hilbert transform (HT) and Kramers-Kronig (KK) integral transform (KKT) method, when applied with NFFT, provides a robust framework for validating electric circuit and experimental immittance data.
  • Addressing uniform boundedness violations through techniques like SSKK or MSKK is crucial for comprehensive KKT compliance.
  • Suggested figures of merit can effectively measure the success of numerical validation for IS data, ensuring physical realizability.