Two-Dimensional Fourier Transform
Omer Demirkaya, Musa H. Asyali, Prasanna K. Sahoo · 2008
We include a short discussion of this relatively classical subject of image processing for the sake of completeness. Because there is already a wealth of literature on the topic, our coverage will be somewhat limited. Here, we will assume that the reader is already familiar with the topic of sinusoidal signals and the one-dimensional (1-D) Fourier transform (FT). For a good refresher on this topic, we recommend the famous Signals and Systems book by Oppenheim, Willsky, and Nawab [1]. The idea behind the FT is to represent the temporal (time) or spatial (space) variations in signals in terms of some sinusoidal basis functions (i.e., sinusoidal signals of different frequencies). This way, the information contained in the signal (in the original domain) could be exactly transformed into spectral information in the frequency domain. Going back and forth between these two domains is possible with the forward and inverse FTs, which we will discuss shortly.