MATLAB Implementation of Fast Fourier Transform (FFT) with Customizable Parameters

In this documentation, I will demonstrate how to implement Fast Fourier Transform (FFT) using MATLAB. FFT is a powerful algorithm that converts signals from time domain to frequency domain, enabling spectral analysis and frequency component identification. The implementation utilizes MATLAB's built-in fft() function which employs the Cooley-Tukey algorithm for efficient computation with O(n log n) complexity. You can customize equation parameters according to your specific requirements, such as sampling frequency, windowing functions, and zero-padding options. Key implementation steps include: 1) Preprocessing input signals with windowing functions (e.g., hamming, hanning) to reduce spectral leakage, 2) Applying fft() with optional length specification for zero-padding, 3) Computing magnitude spectrum using abs() and phase spectrum using angle() functions. This approach allows for customized signal analysis and processing, making MATLAB an ideal platform for understanding and manipulating signal data through frequency domain transformations.