Abstract:
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The successful application of impedance spectroscopy in daily practice requires accurate
measurements for modeling complex physiological or electrochemical phenomena in a single
frequency or several frequencies at different (or simultaneous) time instants. Nowadays, two
approaches are possible for frequency domain impedance spectroscopy measurements: (1)
using the classical technique of frequency sweep and (2) using (non-)periodic broadband
signals, i.e. multisine excitations. Both techniques share the common problem of how to
design the experimental conditions, e.g. the excitation power spectrum, in order to achieve
accuracy of maximum impedance model parameters from the impedance data modeling
process. The original contribution of this paper is the calculation and design of the D-optimal
multisine excitation power spectrum for measuring impedance systems modeled as 2R-1C
equivalent electrical circuits. The extension of the results presented for more complex
impedance models is also discussed. The influence of the multisine power spectrum on the
accuracy of the impedance model parameters is analyzed based on the Fisher information
matrix. Furthermore, the optimal measuring frequency range is given based on the properties
of the covariance matrix. Finally, simulations and experimental results are provided to validate
the theoretical aspects presented. |