How do I create a spectral view for wav files?

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Greetings all. I'm currently coding a multimedia-related program that
will deal with wav files. My program will have a display on which the
wav file will be visually represented, similiar to Cool Edit and other
audio editing programs. Normal waveform display is pretty simple; it's
basically just measureing the peaks of the audio data. However, I'd
also like to implement what Cool Edit calls "Spectral" view. Cool
Edit's help file describes this view as time being the X-axis,
frequency being the Y-axis, and amplitude being the Z-axis (represented
by colors of varying brightness, dark blue to red to bright yellow). I
can't quite figure out how I'm supposed to code that. Can anyone
describe in more detail exactly how a spectral view is calculated, or
perhaps link me to a page that would help me out in this regard?

.

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