Doepfer

Hi Silas,

Well three of us have arrived at that figure independently, so I'm 
reasonably confident it is good. I have now also checked it against 
the 19-stage linear FSR equivalent, and that agrees too. Since I *do* 
have the polynomial for the 19-stage sequence, I'm working on how to 
derive the sequence length analytically, but it is taken a while to 
get back up to speed - it was about 10 years ago I last looked at all 
this stuff.

The circuit is very interesting, as whilst it is certainly not a 
linear FSR in the usual sense (I can't work out if it is non-linear 
or just 'inhomogeneous', but in either case, most of the established 
theory will probably not be applicable), it very capably produces a 
good long sequence, and does not need any special circuitry to kick-
start it into action (the inverter in the feedback loop sees to that).

So far I've tracked it down to 3 other places:

- Ken Stone's CGS Digital Noise (probably later than the A-117)
- A book by Ray Marston: 'Integrated Circuit and Waveform Generator 
Handbook' (1990)
- and the Transcendent 2000 (circa 1978?)

I suspect it is originally from some short paper published ages ago 
(perhaps in something like 'Electronics Letters') - I just wish I 
could track the exact reference down, and save me probably a deal of 
work!

Tim

--- In Doepfer_a100@yahoogroups.com, "Silas Johansen" <sijodk@...> 
wrote:
>
> Tim,
> 
> I'd be willing to bet you a patch-cord that those minus 4 comes 
from a
> miscalculation somewhere. It would be a lot easier to designing an
> algorithm or a circuit with a cycle length of 2^18 straight than
> 2^18-4 as for the latter you would need to reset the bit pattern at 
a
> specified point. With two 4 bit shift registers and two 5 bit ones 
you
> might conceivably design one with a length of (2^4-1)^2 * (2^5-1)^2
> but even this would be harder than designing one with an exact 
length
> of 2^18 and there would be no good reason to do it (at least not for
> the purpose in question)
> 
> /Silas
> 
> On Tue, May 6, 2008 at 11:20 PM, Tim Stinchcombe
> <timothy@...> wrote:
> >
> >
> >
> >
> >
> >
> > > I'm now pretty sure the sequence is at least 2^19 = 524288 
long, so
> >  at
> >  > 1kHz (approx knob setting 4), it will take nearly 9 minutes to
> >  repeat.
> >
> >  With a little computational help from the kind people on the 
Synth DIY
> >  list, and some cajoling to get me to run some calcs myself, I can
> >  confirm that the sequence length is actually 262140 = 2^18-4. 
Kind of a
> >  strange number, but I'm working on shedding some light on it!
> >
> >  Tim
> >
> >
>