什麼是 fast fourier transform ??

Fast Fourier Transform is just a term for a method to calculate Fourier Transform.
http://en.wikipedia.org/wiki/Fft

The Fourier Transform itself is a transformation from a function f(t) to another function F(w).
http://en.wikipedia.org/wiki/Fourier_analysis

As math, it does not have a meaning. In practice, f(t) is usually a function of time. That means it is a waveform. F(w) is function of frequency. In short, you input w (a frequency) and F(w) gives you the amplitude of this frequency in the original waveform.

For example, if someone talk in high pitch, you may not notice anything special in the recorded waveform f(t). But after transforming to F(w), if you plot a graph of F(w) you see high values in high frequencies.

The wavelet analysis is a similar concept but deeper. Therfore you need to know Fourier Transform first.
http://en.wikipedia.org/wiki/Wavelet_analysis

Reference book (if you are university student in engineering field):
Introduction to communication systems
Stremler, Ferrel G.

大學級數,數學好差好難明白