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
> >
> >
>