additive

[Martin Czech]

> well, thats not what they are teaching in engineering school these days!
> They say that (loosely quoted from textbook) "Any sound can be broken up
> into its harmonic series using fourier analysis. Once these basic
> frequencies and amplitudes are known, then, all that needs to be done to
> replicate the original sound is to do a time domain analysis of the
> amplitude changes of each of the various harmonics." 

I'd say this has two sides:
First the textbook is right, IT CAN BE DONE. You simply FFT window after window
after that you take the IFFT and attach window to window. This is trivial,
of course the signal is the same after this procedure, but only (!) if no
window function (like Hamming, Kaiser, Blackman ...) are applied to
the windows.

But there is the other side as well:  Does the above mentioned method
of FFTing with no window function make sense in the meaning of spectral
content ? I'd say no! Chopping the signal into window chunks creates
(artificial) discontinuities, if you treat a long sine wave sample,
you'll get very strange "spectra", this is clear , because after
chopping the signal is no sine wave any more. If you wan't to have a
meaningfull spectral representation, you'll have to apply a window
function w(t), and this means convolution with the spectral equivalent
W(s), ie. smearing.  This smearing or unsharpness will hide the little
dirty "harmonics", that makes the sound of instruments so interesting.

Does this remind you of something? It is the Heisenberg theorem applied
to music instead of quantum physics (the math is the same in this
case):  time resolution rivals with spectral resolution. If you want
good spectral resolution, the window has to be very long, thus time
resolution suffers and vice versa.

I had to learn this the hard way, when I wrote this little program
to feed my microwave with wavetables (a poor man's wave).

So, with this perspective: NO, IT CAN'T BE DONE.

m.c.