Two-Dimensional Discrete Fourier Transform Implementation

We have successfully implemented the Two-Dimensional Discrete Fourier Transform (2D DFT) using MATLAB. This transformation serves as a powerful mathematical tool that converts discrete time-domain signals into frequency-domain representations, enabling detailed analysis of signal spectrum characteristics. The implementation utilizes MATLAB's built-in fft2() function, which efficiently computes the 2D Fourier transform using the Fast Fourier Transform (FFT) algorithm, significantly reducing computational complexity from O(N²M²) to O(NM log NM) for an N×M matrix. Through this transformation, we gain enhanced understanding of signal frequency components and energy distribution patterns, providing fundamental support for research in signal processing and pattern recognition. Our implementation leverages MATLAB's comprehensive function library and user-friendly interface, incorporating additional features such as zero-padding for frequency resolution adjustment and fftshift() for proper frequency domain centering. The code structure includes preprocessing steps for data normalization and post-processing for magnitude spectrum visualization using abs() and log scaling. This project not only deepens our understanding of discrete Fourier transform principles but also demonstrates proficiency in MATLAB's computational capabilities. The implementation includes optimized memory handling for large datasets and incorporates practical considerations like windowing functions (e.g., Hann window) to reduce spectral leakage. The resulting frequency domain analysis enables applications in image processing, compression algorithms, and feature extraction techniques.