band limited oscillators

[Tony Hardie-Bick]

Hey Marc,

The theory is, er, easier than the code for it, at least if you're talking about 
optimal code. But there are (I vaguely recollect) plenty of cheesy shortcuts, 
especially if you've got some MBs of RAM to spare.

To avoid that whole pseudo-fir shortcut madness, you could just use sinewaves 
with phase-modulation feedback, ie, same as DX7 et al, but do it with much finer 
control of the feedback levels. A single sine with phase mod FB can give you a 
sawtooth. A couple in series can be detuned to get a bit of beef. Add a ring 
modulator, pan all the outputs in different positions, etc etc, gets 
interesting. Variably distort the phase of the address to get chorus, etc. Cheap 
on CPU.

But if you want square and PWM proper, you will need the 
fir-whatsitcalled-supersampling theory thing er, whatever. It is fun. Never 
wrote any - it's one thing that yer average digital synth does quite well (Nord 
Lead was the first to do a decent job).

My approach was to hack it from first principles, considering a high quality 
fractional sample rate converter, what happens if you put a step through it at 
various fractional sample offsets, and then you'll need some math sim package to 
help you calculate the optimal pulse decay length and coefficients for your 
preferred S/N ratio. I found doing all this much easier than reading any of the 
technical papers on the stuff. The CPU overhead increases the more switching 
from plus to minus goes on, so, CPU overhead increases with frequency, where the 
overlap in pulse-decay sinusoids starts to get a bit alarming.

Having done a quick search just now, I feel as if I understand it less than I 
did five minutes ago... Man - why do they make everything so *complicated*.

Tony (HB)


M-.-n wrote:
>  
> I’ve decided to expand my horizon by exploring the world of band limited 
> oscillators. Has anybody good links for theory/implementation ?
> 
> Thanks
> 
> M.
> 
> 
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