Practical Programming Tutorial of Two Dimensional Discrete Fourier Transform (DFT) Based on MATLAB® for Both 2D Signals and Images

Abstract

The two-dimensional (2-D) Discrete Fourier Transform (DFT) and Inverse Discrete
Fourier Transform (IDFT) represent mathematical models for 2-D signals (such as digital
images and digital videos) in the frequency and spatial domains, respectively. Digital Image
Processing (DIP) has been implemented globally over the past two decades. Thus, 2-D
Discrete Fourier Transform (2-D DFT) is essential in terms of representing mathematical
models and analyzing 2-D signals and systems. In light of its importance, this article
presents a tutorial for 2-D DFT utilizing MATLAB® for both 2-D signals and images. The
analysis of the discrete signals are based on both spatial and frequency domains. The
theoretical basic of 2-D DFT is presented, followed by a tutorial based on synthetic and
real examples using MATLAB®.