Welcome to the Fourier Analysis tutorial. This tutorial explains the Fourier transform and Fourier series, both staple parts of advanced mathematics, essential for many science and engineering tasks.
"HLT" referenced herein refers to "Engineering Tables and Data", 2nd edition, by A.M. Howatson, P.G. Lund, J.D. Todd, August 1991, ISBN 0-412-38970-3. Unfortunately, this data book is now out of print.
For other perspectives on the subject, and related subjects such as wavelet analysis and z-transforms, try:
http://www.mathtools.net/ - a technical computing portal
http://engineering.rowan.edu/~polikar/WAVELETS/WTtutorial.html - a tutorial on wavelet analysis, including a bit about the Short Time Fourier Transform
http://www.auto.tuwien.ac.at/~blieb/woop/fft.html - a non-recursive FFT algorithm.
- Java applet showing Fourier approximations for arbitrary functions.
http://www.cs.caltech.edu/~frazier/cs20/c/lab2/Lab.html - a Java applet (with source) for doing recursive FFTs, inverse FFTs, and polynomial multiplication.