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Algorithms for reconstruction of impedance spectra from non-uniformly sampled step responses

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Fig. 1

Example of stimulus and response signals. A: Stimulus B: Step response.
Example of stimulus and response signals. A: Stimulus B: Step response.

Fig. 2

Error of simplistic sampling instant estimation and its correction. A: Dependency on time constant of exponential signal and on sampling interval. B: Example of correcting the error.
Error of simplistic sampling instant estimation and its correction. A: Dependency on time constant of exponential signal and on sampling interval. B: Example of correcting the error.

Fig. 3

Derivatives of the straightforward local approximations.
Derivatives of the straightforward local approximations.

Fig. 4

Local signal approximations used to reconstruct measured signal.
Local signal approximations used to reconstruct measured signal.

Fig. 5

Simulated errors of time rescaling for single exponential signals. Reconstruction of measured signals is done by shape-preserving splines.
Simulated errors of time rescaling for single exponential signals. Reconstruction of measured signals is done by shape-preserving splines.

Fig. 6

Local signal approximations with and without time rescaling for spheroid in nozzle. A: Whole spectrum. B: Zoom at higher frequencies.
Local signal approximations with and without time rescaling for spheroid in nozzle. A: Whole spectrum. B: Zoom at higher frequencies.

Fig. 7

Model parameters after fitting the measured electrical signals for spheroid in the chamber. A: simple fit of the distribution of relaxation times model and B: the same model fit with proposed improvements.
Model parameters after fitting the measured electrical signals for spheroid in the chamber. A: simple fit of the distribution of relaxation times model and B: the same model fit with proposed improvements.

Fig. 8

Local signal approximations for spheroid in nozzle. A: without correction. B: with correction.
Local signal approximations for spheroid in nozzle. A: without correction. B: with correction.