[sdiy] FM math question

[Mattias Rickardsson]

A saw core vco with a saw->tri->sin shaper is a vc sine oscillator.
You then modulate this sine with another sine, and get an appropriate result.

Am I missing something?

/mr


2008/10/15, Ian Fritz <ijfritz at comcast.net>:
> This is a question concerning my new FM (technically PM, of course)
> VCO.  It uses a sawtooth core waveform, modulated by anything, but we can
> assume a Sin modulation for now.
>
> It's easy enough to calculate the output spectrum -- just Fourier transform
> the Saw and apply the standard FM equation to each component.  But my
> question is about what happens after that signal is passed through two
> waveshapers, first a Saw -> Tri shaper, then a distortion circuit for Tri
> -> Sin.
>
> Has anyone looked at how to do the math for this
> waveshaping?  Conceptually, I suppose you might be able to express the
> output of the VCO core as a sum of sawtooths, look at the effect of the
> first shaper on each and then express that result as a sum of triangles and
> then look at the effect of the second shaper to those.  The problem with
> that approach is that the various input signals to each shaper will have
> differing amplitudes, so the effects of the shapers are not simple.
>
> The reason I am asking this is that I seem to be getting a surprising
> result: the final output looks as if it has (at least roughly) the same
> harmonic components as would a modulated Sin wave having the same frequency
> as the Saw!  In other words, the strongest frequency components of the
> output are at the fundamental frequency of the VCO plus or minus multiples
> of the modulation frequency.
>
> How can this come about?  It seems to imply some sort of commutivity
> between the the nonlinear modulation process and the nonlinear waveshaping
> process.  Am I missing some simple way to look at this result?
>
> I posted a couple of clips using the Sin shaper output here:
> http://electro-music.com/forum/topic-29149-25.html
> You should be able to hear that the harmonic content is much more subdued
> than that of the raw sawtooth output (clip on previous page).
>
>    Ian
>
> _______________________________________________
> Synth-diy mailing list
> Synth-diy at dropmix.xs4all.nl
> http://dropmix.xs4all.nl/mailman/listinfo/synth-diy
>