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 method is the standard method for the calculation of numerical Fourier transform and then the impedance of electrochemical systems. However, the presence of noise in the data results in a high error rate in calculating the numerical Fourier transform. Therefore, to reduce the error rate in noisy conditions, the solution order of the Fourier transform can be increased. In the present paper, the solution order for calculating the numerical Fourier transform in the presence of noise has been raised using a straight line, second and third-order polynomials; afterward, the impedance of series, parallel, and battery circuits is calculated. Additionally, the higher order solutions’ calculated impedance is compared to the acquired impedance in the FFT method in noisy conditions. We conclude that increasing the solution order of numerical Fourier transform from zero to one leads to good results, but further enhancement of solution order deteriorates the responses. Therefore, the linear method is the best way for calculating the numerical Fourier transform in the presence of noise.