Statistical Analysis of the Measurement Noise in Dynamic Impedance Spectra.

Area of Science:

• Electrochemistry
• Data Analysis

Background:

• Dynamic impedance spectra acquisition during cyclic voltammetry involves fitting models with weighted non-linear least-squares minimization.
• Weighting factor selection significantly impacts parameter extraction accuracy.
• Dynamic impedance measurements under non-stationary conditions are susceptible to analog-to-digital conversion errors.

Purpose of the Study:

• To develop a rigorous method for evaluating weighting factors in dynamic impedance spectroscopy.
• To account for measurement errors in non-stationary electrochemical systems.
• To improve the reliability of parameter extraction from dynamic impedance spectra.

Main Methods:

• Calculated the expected variance of immittance errors considering time-varying measurement procedures.
• Assumed constant variance and uncorrelated noise in voltage and current signals.
• Used the calculated variance to determine optimal weighting factors for least-squares fitting.
• Employed Padé approximants as a transfer function measurement model.

Main Results:

• The derived variance expression accurately captures the frequency dependence of residuals.
• The proposed weighting method reliably performs complex non-linear least-squares fitting.
• Demonstrated effectiveness on two classical electrochemical systems.

Conclusions:

• The developed variance calculation provides a rigorous basis for selecting weighting factors in dynamic impedance spectroscopy.
• This method enhances the accuracy and reliability of parameter extraction from dynamic impedance data.
• The approach is suitable for analyzing electrochemical systems under non-stationary conditions.