[music-dsp] Article: antialiased sine waveform syncing

Vadim Zavalishin vadim.zavalishin at native-instruments.de
Mon Jun 8 09:04:31 EDT 2009

> Also it doesn't really provide _any_ useful generalization which
> renders it mathematically useless - performing analytical calculations
> doesn't reveal anything to us about the underlying symmetry and
> structure of the problem.

Well, I don't know what do you mean by "mathematically useless". However the 
methods definitely work in practice, as you can see by the spectrum diagrams 
at the end of the article (also I have built a test implementation in 
Reaktor Core which is available in Reaktor user library). Also, the first of 
the three described methods is actually an obvious generalization of the 
BLEP sync antialiasing method. Is the latter then also "mathematically 
useless" in your opinion as well?

> Some time ago, as you already know well as we had some chat on another
> forum, I released an article on the general problem of the efficient
> bandlimiting of oscillator hard-syncing; that of arbitary waveform
> hard sync. I provide the link again here:
> http://s1gnals.blogspot.com/2008/12/bloo_6897.html

I've read that article. My main problem with it is that it doesn't provide 
any practical analysis on how "wrong" the resulting spectra are going to be. 
I was too lazy to do the respective analysis myself.

> One interpretation of this theorem is that we can approximate a
> function (let's stick to one variable without loss of generality) by
> knowing the derivatives at one single point. In a similar manner we
> can bandlimit a generic hard-sync case by bandlimiting higher order
> derivatives of a Cn discontinuity through integration

That's exactly the first of the methods described in my article.

Thanks for the suggestion on the integrator replacement technique BTW.


Vadim Zavalishin
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