On the physical definition of dynamic impedance: How to design an optimal strategy for data extraction

Dynamic electrochemical impedance spectroscopy (DEIS) has attracted the interest of researchers due to its capability of acquiring impedance spectra of non-stationary systems in a broad range of frequencies. Although developed in the 70's, a physical definition of dynamic impedance, and in general of dynamic transfer function, is not present in literature. In this manuscript the general concept of dynamic frequency response is given in correlation to the Volterra series expansion: this can be used to define the ideal dynamic impedance response of an electrochemical system. It is clarified that DEIS is the intermodulation of the ac signal with the dc signal. Starting from this, different strategies for the extraction of the dynamic impedance spectra are compared, which are based on different heuristic definitions of DEIS. There are two main methodologies, one based on the use of window functions and the other on quadrature filters. Limits and merits of the different methodologies are discussed in the frame of the data analysis and data handling and show that window functions suffers at recovering low-frequencies impedances while quadrature filters work best in experiments which have a periodic or quasi-periodic trend.