MATLAB Implementation of FFT Algorithm for Signal Analysis

In this article, we explore the implementation of FFT algorithms for triangular waves, sine waves, and square waves using MATLAB. We conduct an in-depth analysis of frequency spectra for square wave and triangular wave signals, while examining how sampling points and sampling frequency affect spectral resolution. The implementation involves generating waveforms using functions like sawtooth() for triangular waves, square() for square waves, and sin() for sine waves, followed by applying the fft() function with proper normalization and frequency axis calibration. We investigate how varying the number of sampling points (N) influences frequency bin spacing through the relationship Δf = fs/N, where fs represents the sampling frequency. The analysis includes windowing techniques to reduce spectral leakage and proper zero-padding strategies for improved frequency resolution. Through exploring these concepts using MATLAB's signal processing toolbox, we gain deeper insights into digital signal processing and spectral analysis, enabling practical application of this knowledge to solve real-world signal processing challenges. The code implementation includes visualization using plot() and stem() functions to display both time-domain waveforms and their corresponding frequency spectra.