Fast Fourier Transform (FFT) Implementation on Input Images

This documentation explores the implementation of Fast Fourier Transform (FFT) for input images using MATLAB. The Fast Fourier Transform is a mathematical algorithm that decomposes complex signals or images into constituent sine and cosine functions. By applying FFT to images, we obtain spectral information that reveals various frequency components within the image data. This guide demonstrates how to utilize MATLAB's built-in FFT functions (such as fft2() for 2D images) to perform this transformation, including proper zero-padding and frequency shifting using fftshift(). We'll examine practical implementation aspects like handling complex outputs through magnitude spectrum calculation (abs()) and phase spectrum (angle()). The discussion extends to interpreting spectral results for applications such as frequency domain filtering, noise analysis, and image compression techniques. Through this comprehensive overview, readers will gain deeper understanding of FFT's critical role in digital image processing and its practical implementation using MATLAB's computational framework.