Low-Complexity RDFT-Based Impedance Calculation for Enhanced EIS Analysis

EIS is a measurement method based on spectrum analysis to obtain impedance changes indirectly. Therefore, an efficient and rapid Fourier transform is significant. This study proposes a low-complexity and high-throughput recursive DFT architecture based on the Chinese remainder theorem decomposition method. Compared with previous works or the Goertzel architecture, this study has the following advantages when the frame size $(N)$ is $5,000: 1$) After normalization, addition and multiplication save at least $87.5 \%$ and $87.5 \%$ respectively, significantly reducing computational complexity; 2) Due to architectural features, the number of recursions can be reduced to one-eighth, effectively improving calculation accuracy; 3) The throughput capacity is increased eightfold, shortening the conversion time. The proposed architecture is simple and requires only one real multiplier, four real adders, and two constant multipliers for hardware accelerator designs. This is advantageous for real-time analysis applications in composite stimulation signals or extracting a few bins in broadband stimulation signals. In the future, it can also be combined with sensors to realize various EIS applications in IoT.