An Introduction to Fourier Theory
A mathematically inclined introduction with illustrations and explanations of related theorems, its properties and numerical methods for calculating transforms.
Fast Fourier Transforms
Survey and history of FFT algorithms from Wikipedia.
Introduction to the Fourier Transform
Notes on applications to Image Processing.
Mathematics of the Discrete Fourier Transform (DFT
Notes by Julius O. Smith III, Stanford.
The FFT Demystified
A web text explaining the techniques of discrete and fast transforms.