Investigating the effect of noise and solution order on calculating the impedance of electrochemical systems using impedance spectroscopy in the time domain.

Fast Fourier Transform (FFT) is a standard method for calculating the numerical Fourier transform as well as the impedance of electrochemical systems. However, the presence of noise in data increases the error rate while calculating the numerical Fourier transform and in order to reduce the error rate in noisy conditions, the solution order of the Fourier transform should be enhanced. In the present study, the solution order used for calculating the numerical Fourier transform in the presence of noise was enhanced using a straight line and then second- and third-order polynomials. Next, the impedance of the series, parallel, and battery circuits was calculated. Additionally, the calculated impedance of the higher-order solutions was compared to the acquired impedance through the FFT method in noisy conditions. The findings of this study demonstrated that increasing the solution order of the numerical Fourier transform from zero up to one would yield satisfactory results; however, further enhancement would deteriorate the outcome responses. Therefore, it can be concluded that the linear method is the best way for calculating the numerical Fourier transform in the presence of noise. [ABSTRACT FROM AUTHOR]