[sdiy] Synth waveforms

[Richie Burnett]

When looking at the classic synth waveforms one *could* say that they are 
all really just filtered versions of each other...

The square and pulse waveforms are comb filtered versions of the sawtooth 
waveform.  (When the comb filter delay is equal to half the period, all of 
the even harmonics get notched out.  Similarly interesting spectra result 
from other comb-filter delays / pulse widths.)

The triangle waveform is a low-pass filtered (integrated) version of the 
square waveform, so that it's harmonics roll-off at twice the slope.

The parabolic waveform is a low-pass filtered (integrated) version of the 
sawtooth waveform, so that it's harmonics roll-off at twice the slope.

And if you want to go back to first principles the sawtooth waveform is 
really a low-pass filtered (integrated) impulse train.  (The comparator in 
your VCO provides the infinitesimally short pulses that reset the 
integrator.)

The impulse train is like where it all starts.  (A block of plain marble 
from which something sonically interesting can be carved out.)  It has all 
harmonics present with equal amplitudes.  You can get any other static 
periodic waveform by applying a (sufficiently complex) filter to the impulse 
train to carve it's harmonic spectrum into whatever you want.

-Richie,