Using least squares and Kramers-Kronig transforms in the processing of impedance spectroscopy measurement data

Abstract

The paper presents a novel method for improving the reliability of impedance spectroscopy. This is achieved by combining the least squares (LS) method and Kramers-Kronig (KK) transforms when estimating the parameters of the measured sinusoidal response. The simplest idea in spectroscopy measurement is to use LS approximation at each measurement frequency, thus obtaining the impedance spectrum. This approach, however, does not include information on the correlation between the imaginary and the real parts of the impedance. Thus the results may be of low quality in the presence of noise. Incorporating KK transforms into the verification process of measured impedance can improve its quality. However, a better idea is to combine KK transforms and the LS method into one approximation procedure. Such an approach gives better results than using both methods separately. This has been proved by a simulation study which assumes that noise is additive and that the signal-to-noise ratio (SNR) can vary greatly. The advantage of the proposed method is more evident in the case of lower values of SNR. However, in order to obtain an improvement the frequency used in examination should cover almost the whole impedance spectrum. The quality of the combined method also depends on the number of frequencies used. For the noiseless signal the LS approximation gives better results than the combined method because of the error of numerical integration, which is relatively high. © Springer-Verlag 2007.