Application of Fast Fourier Transforms in Some Advanced Electroanalytical Methods

Abstract

In the most of electrochemical (EC) experiments, measurements mostly are performed in the time domain. However, in some cases, we require more information for the obtained data such as knowledge about the frequency content and behavior of the electroanalytical signals and of complete systems. Fortunately, there exists a defined method for transforming data from the time domain into the frequency domain, where information exist about the spectral content of EC data. The method for this propos is Fourier Transform (FT), which has the ability to convert a time domain data to the complex frequency domain, meaning the spectral data contains information about both the amplitude and phase of the sinusoidal components that make up the signal. In addition, the inverse FT, converts the generated complex frequency-domain signal data back into the time-domain without losing wanted information. Accordingly, it can say that both the timeand frequency-domain data complement and the two domains can provide a different view of the same EC data. Application of fast Fourier transformation (FFT) algorithm for numerical EC data provides the complex spectrum according to magnitude and phase, which can be used for real time analysis. In this direction, in modern electrochemistry, FFT has been used for digital signal processing and filtering. Also, the FFT process returns a vector of real and imaginary elements, which represent the various resolved harmonics in impedance spectroscopy, AC and square wave voltammetry (Popkirov, 1996). On the other hand, it must be noted that in all EC data collection, to hold on the sampling theorem for FFT, the bandwidth of the input signal is limited by an analog low pass filter (cutoff frequency fc = fin,max) ahead of the Analog to Digital (A/D) converter. In fact, after collecting data in the computer memory, they are used for calculating the signal in the frequency domain. This chapter serves as summary application of the FFT analysis techniques implemented in EC measurement platform. By reading through this document, you will receive a comprehension of the fundamental concepts in FFT-based measurements used throughout EC application, providing you insights to better understanding of the measurement