MATLAB Code Implementation of Fast Fourier Transform

This document provides a MATLAB implementation of the Fast Fourier Transform (FFT) algorithm accompanied by sample test data. The Fast Fourier Transform is a fundamental signal processing technique widely applied in audio processing, image analysis, video compression, and various engineering fields. The implementation utilizes MATLAB's built-in fft() function, which employs the Cooley-Tukey algorithm to efficiently compute the discrete Fourier transform of signals with O(n log n) computational complexity.

The program includes proper data preprocessing steps such as signal windowing and zero-padding to minimize spectral leakage and improve frequency resolution. Key functions demonstrated include fft() for forward transformation, ifft() for inverse transformation, and fftshift() for frequency domain rearrangement. The provided test data contains sample signals with known frequency components, allowing users to validate the implementation and observe characteristic frequency domain patterns.

This resource is designed to help researchers and engineers quickly process temporal data and gain deeper insights into frequency domain analysis. The code includes comments explaining parameter selection, normalization requirements, and practical considerations for real-world applications. We hope this implementation enhances your understanding of FFT principles and facilitates advanced signal processing projects.