High Precision, Low Complexity, and Fast Calculation Based on Hybrid Recursive DFT and FFT Algorithms for Electrochemical Impedance Spectroscopy System

This study presents a novel hybrid algorithm merging recursive discrete Fourier transform (RDFT) and fast Fourier transform (FFT) to meet the demands of electrochemical impedance spectroscopy (EIS) applications. It particularly addresses scenarios where users need to calculate a reduced number or a variable quantity of frequency bins. By offering the flexibility for users to choose either RDFT or FFT based on their specific requirements, the algorithm overcomes the limitation encountered in traditional impedance calculation methods, where the FFT transform length is constrained to being a power of 2. To ensure more precise observation of the device under test (DUT) impedance spectrum, we set the sampling rate (Fs) and transform length (N) to 40960, achieving a frequency resolution of 1 Hz. Unlike the traditional Radix-2 FFT method, the proposed hybrid algorithm eliminates the need for zero padding to supplement the signal to 65536 points. Consequently, the overall computation involves 1163264 multiplications and 2359296 additions, marking a notable reduction of 44.52% in multiplications and 43.94% in additions compared to the traditional radix-2 FFT method’s 2097152 multiplications and 4194304 additions. In order to validate measurement accuracy, experiments were performed using six pure resistors and two RC circuits. The RDFT-based impedance calculations, after averaging all measurements, resulted in magnitude relative error (MRE) and phase absolute error (PAE) values below 0.11% and 0.21°, respectively. Likewise, impedance calculations utilizing the hybrid algorithm showcased even greater precision, with MRE below 0.06% and PAE below 0.09°. These findings highlight the superior accuracy and streamlined complexity provided by the proposed system. For hardware implementation, the system costs only U.S. 352, offering a cost-effective solution for various high-precision EIS measurement applications.