Doepfer

> > Any idea how long is this sequence? Can you notice it repeat when 
> using high frequency clocks?

<<snip>>

> Alas it is some years since 
> I studied such things, as otherwise I could probably have worked out 
> the appropriate polynomial and *told* you how long the sequence is...!

Well, I just couldn't let it rest at that!

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. 
(And at max rate/min setting, approx 68kHz, it will be about 8 seconds, 
but as I said before, at such speeds it is hard to pick up any sense 
of 'structure' to determine that it *is* repeating.)

My previous assertion that the inclusion of the inverter in the 
feedback loop would reduce the 'linear complexity', and hence the 
length of the sequence was in error - if I'm interpreting how to go 
between the hardware gates and the maths correctly, the inverter makes 
the feedback non-linear, by effectively cancelling the feedback from 
the the first tap. Thus the sum of two of the taps is now *multiplied* 
by the third, and this changes everything!

There is however a nifty algorithm, the 'Berlekamp-Massey algorithm', 
which will find the minimum length (= the linear complexity) of a 
linear feedback shift register necessary to generate a given sequence. 
I ran this against another circuit (which I designed and hence I know 
what to expect), and it correctly identifies the feedback taps, so I 
was happy it was working OK, and when run against several 'captured' 
sequences from the A-117 (using my scope, most about 40 bits, the 
longest being 59), and it consistently returns the same taps, and gives 
the linear complexity as 19. I'm having some difficulty with the idea 
that a non-linear shift register of length 18 can produce a sequence 
from a linear one of length 19, but for now I have to trust that my 
computations are correct (at least they look pretty compelling!).

If Dieter is reading this and knows any more detail about where this 
circuit came from, I'd love to hear it!

Tim