FFT Function Implementation for Sine Wave Signal Analysis

This documentation demonstrates the implementation of spectral analysis for sine waves, rectangular signals, and white noise using MATLAB's FFT function. The process begins by passing these signals as input arrays to the FFT function, which computes the Discrete Fourier Transform using a highly optimized Cooley-Tukey algorithm. The resulting frequency domain data is then analyzed to examine spectral components and energy distribution patterns. For sine wave analysis, the FFT output clearly identifies dominant frequency peaks, allowing precise determination of signal frequency and amplitude through magnitude spectrum examination. The implementation typically involves proper sampling rate configuration and windowing functions to minimize spectral leakage. Rectangular signal analysis reveals characteristic sinc-function patterns in the frequency domain, displaying harmonic components and side lobe structures. The code implementation includes zero-padding techniques for frequency resolution enhancement and proper normalization for accurate amplitude measurements. White noise spectral analysis demonstrates flat power spectral density distribution, confirming the signal's broadband characteristics. The implementation incorporates power spectrum calculation using periodogram methods and statistical averaging for noise characterization. Through systematic FFT-based spectral analysis, we gain comprehensive insights into signal properties, frequency content, and spectral behaviors, facilitated by MATLAB's built-in signal processing functions like fft(), fftshift(), and periodogram().