Measurement of cole-davidson diffusion through padé approximations for (bio)impedance spectroscopy

Throughout various engineering applications, measurement science faces the problem that parameters of interest are not directly measurable with a specifically designed instrument. As such, one relies on indirect measurement which is mapped through a mathematical model to the parameters of interest. The parameters of interest are consequently estimated statistically through analyzing the measurements. This field is known as system identification and serves applications in control, mechanical, and biomedical engineering among others. Anomalous diffusion pops up in impedance and dielectric spectroscopy such that the application of system identification techniques in electrochemical, microwave, and biomedical engineering may be affected by diffusion. The presence of diffusion may introduce systematic errors or bias when applying system identification techniques of linear time-invariant (LTI) systems. In this paper, we revisit classical LTI identification in the presence of Cole-Davidson (CD) diffusion wherein we accomplish: 1) detecting the CD diffusion component; 2) discriminating the diffusion from the remaining dynamics; and 3) modeling the CD diffusion through a fractional-order model, in particular, a pole of fractional-order multiplicity.