MATLAB Implementation of Discrete Fourier Transform with Windowed FFT for Harmonic Signal Analysis

This article discusses two fundamental methods: Discrete Fourier Transform (DFT) and windowed FFT, which effectively address spectral leakage and fence effects in harmonic signal analysis. The Discrete Fourier Transform converts time-domain signals into frequency-domain representations, enabling frequency component analysis through mathematical transformation. In MATLAB implementation, this can be achieved using the built-in fft() function, which computes the DFT efficiently using Fast Fourier Transform algorithms. Windowed FFT technique involves applying window functions (such as Hamming, Hanning, or Blackman windows) to signals before performing FFT analysis. This preprocessing step helps reduce spectral leakage by tapering signal edges and minimizes fence effects by improving frequency resolution. In MATLAB code, this typically involves multiplying the input signal with a window function using dot-product operations (e.g., signal.*hamming(N)) before passing it to the fft() function. These methods prove particularly effective for handling spectral issues in harmonic signals, where precise frequency component identification is crucial. The implementation requires careful consideration of parameters like window length, overlap percentage, and window type selection to optimize spectral accuracy while maintaining computational efficiency.