[sdiy] Single chip (3 opamp) wave multiplier

[Martin Czech]

:::Thank you both for your comments. I have very little experience with FM, as
:::I'm sure you can tell. I'm still curious if there could be a mathematical
:::connection between zero-freq-carrier FM and the folded waveforms. Offhand,
:::the math doesn't look related, but if they look the same and sound the same
:::... I am now thinking this might be approached as follows:

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lots of fun for little money)

It looks somehow similar and sounds somehow similar to me.
But we all know that things that sound allmost the same have no
mathematical link, so there is only some little hope...

I must confess that the math close to Bessel expension is very hard
for me, and the math beyond is way over my head. It may well be that
somewhere deep in some library you can find a 100+ years old text exactly
on that matter, and that it is all there, you just need to know a friendly
mathematician of the right "direction" to show you.


m.c.


:::
:::1.) Since the ZFCFM equation has a Fourier expansion with Bessel
:::coefficients that vary all over the map, I wonder if they somehow constitute
:::a complete mathematical set. In other words, given an arbitrary (but odd,
:::for simplicity) periodic function z(t), is there a weighting function g(m)
:::that allows z(t) to be expanded in terms of the ZFCFM's y(t,m):
:::
:::y(t,m) = sin[m Sin(wt)]
:::
:::z(t) = Integral_dm[g(m)*y(t,m)].
:::
:::2.) If the above conjecture is true, then one could expand
:::experimentally-measured folded waveforms and see if there is a predominant
:::value of m in the expansion.
:::
:::I don't have much literature on FM, although I vaguely recall looking
:::through the original Chowning paper when it came out. The Moore book on
:::computer music has some simple standard FM synthesis material, but nothing
:::specifically on ZFCFM.
:::
:::Best regards,
:::
:::  Ian