Fourier Transforms

Abstract

This chapter presents an overview of definitions and theorems for Fourier transforms in the context of computer vision. The presentation is made without any claims on being either thorough or mathematically strict. Some results are stated without proofs and the transforms of various functions are assumed to exist without further ado. For a more rigorous treatment of these issues, see, for example, [23]. Furthermore, it is assumed that the reader is familiar with the one-dimensional Fourier transform, both the continuous version and the discrete Fourier transform, as well as some mathematical constructions such as generalized functions or distributions.