
Chapter 7
The Fourier Transfor m
7.1 Introduction
The Fourier Transform is of fundamental importance to image processing. It allows
us to perform tasks that would be impossible to perform any other way; its efficiency
allows us to perform other tasks more quickly. The Fourier Transform provides, among
other things, a powerful alternative to linear spatial filtering; it is more efficient to use the
Fourier Transform than a spatial filter for a large filter. The Fourier Transform also allows
us to isolate and process particular image “frequencies,” and so perform low pass and high
pass filtering with a great degree of precision.
Before we discuss the Fourier