Tom Austin wrote:

> Just like what I had in school - professor was a brain on feet, but no 
> practicable applications really shown or taught.

Our brain on feet was called Zimin Wu. His English was... minimal. Which 
is kind of an impediment to teaching, actually. (Fortunately, this was a 
lecture in HCI, not mathematics.)

> As you probably already know, DSP systems use the transforms a lot and 
> can actually be quite fun.
> 
> We did type a few transforms into MATLAB and get to hear what it did to 
> a sound file, but little more.
> 
> What I really wanted was to be able to do it on a chip and then have it 
> process sound real-time.  That would have helped me see the application 
> much more clearly.

Go here:

http://www.falstad.com/mathphysics.html

Scroll down to "signal processing".

They have two applets. One lets you draw an arbitrary waveform and see 
its Fourier series, draw an arbitrary Fourier series and let you see its 
waveform, and listen to the result in either case.

They also have a little DSP applet which will let you play [literally!] 
with any kind of FIR or IIR filter known to mankind - not just the usual 
type-I Chebyshev filter, but also type-II, for example. See and hear in 
realtime, tweak the parameters, and so forth.

That single page also has links to a ridiculous number of other 
addictive applets, like wavetank simulators, circuit simulators, and God 
only knows what else. You might not leave for several hours.

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