Portable RDFT-Based EIS System Design With a Low-Complexity Impedance Calculation

Abstract

This paper presents a novel low-complexity impedance calculation based on a compact recursive discrete Fourier transform (RDFT) for electrical impedance spectroscopy (EIS) system design. Compared to a traditional fast Fourier transform, an arbitrary-length RDFT is not limited by the power-of-two transform length. By choosing a suitable integer ratio of the desired frequency/frequency resolution, the spectrum leakage can be significantly reduced by 4-Hz resolution per bin, which enables a lower magnitude relative error (MRE) and a phase absolute error (PAE) in impedance calculations. Here, the practical measurement results show that the maximum MRE and PAE are below 0.1% and 0.5°, respectively, making this approach superior to previously reported ones. Compared with the state-of-the-art Goertzel filter-based EIS system, the proposed method provides more frequency bins (+43.75%) within the same frequency band, and the operations in terms of square root, division, and arctangent are drastically reduced by 50%, 33%, and 50%, respectively. In addition, the proposed system only costs $474 USD and can serve as a suitable solution for various EIS applications in the future.