I'll have another go at summarising FFT for beginners (of which I count as
one).  As I mentioned, please ignore the previous attempt!  Here goes:

The highest frequency you can extract is half the sampling
frequency.  In other words, if you sample at 10kHz then the highest
frequency you can pull out is 5kHz (this is known as the Nyquist frequency).

The lowest frequency you can extract is 1 / duration of sound bite.  So, if
your soundbite is 100ms long, then the lowest frequency you can extract is
10Hz.  With a 2 second long soundbite your lowest extractable frequency is
0.5Hz, and so on.

The rest of the steps in the FFT output are multiples (harmonics) of that
lowest frequency.  So, with our 100ms soundbite the first item in the FFT
output represents 10Hz, the next represents 20Hz, and so on up to the
Nyquist frequency.  (This is just a better way of explaining what I said in
my previous attempt).

Most FFT engines require you to present them with a soundbite which is
exactly a power of 2 samples long.  In other words, the soundbite must
consist of 4, 8, 16, ........ 256, 512, 1024, 2048, etc samples.  If your
soundbite isn't the right length, you can either truncate it down to the
previous power of 2, or you can pad it with zeroes up to the next power of
two.  For example, if your soundbite is (say) 700 samples long you must
either chop it back to 512, or pad it to 1024.  Generally padding is the
better bet if you can spare the processing time.  Both can cause
complications if you are using a "window" (which is too heavy to go into
now).

The industry standard sampling rates we tend to use (e.g. 11025Hz, 22050Hz,
etc), combined with the need to adjust the length of the soundbite to be a
power of 2, means that the frequencies in the FFT output are usually
fractional numbers rather than integers.  For example, a soundbite of 1024
samples, which was recorded at 11025Hz, gives us a bottom frequency of
10.766Hz, the next frequency is 21.533Hz, and so on up to 5512.5Hz.

Finally, to repeat: filter out everything above the Nyquist frequency
*before* you do the sampling.  In other words, the filtering needs to be
done in the analogue domain.  For example, with a 11025Hz sampling
frequency, you would filter out everything above 5.5kHz.  The reason for
this is that frequencies above the Nyquist frequency get "mirrored" back
into the 0 to 5kHz range and give you misleading results.

Steve Thackery
Suffolk, England.
Web Site: http://www.btinternet.com/~stevethack/