Junction Noise

[Magnus Danielson]

From: "jhaible" <jhaible at debitel.net>
Subject: Re: Junction Noise
Date: Thu, 7 Sep 2000 00:55:08 +0200

Somehow I think we have come far of the junction noise (look at the thread
subject) and wandered into the wonders that governs discrete math and which
theories we fall back upon when we do random generators in digital.

> If you just play your PRN sequence _once_, you should have a continuous
> spectrum.

There are more things that needs to be ideal, but never the less...

> (But only for a limited time, unfortunately.)

Yeap. Most unfortunatly so. It would solve a hell of a lot of powering problems
too.

> The more often you repeat the same cycle, the less "smearing" you will get,
> and
> at infinite repetition you'll have discrete frequencies.
> So altering the sequence, or the playback speed of the same sequence,
> between
> every cycle, must surely help to preserve the "smearing".

Correct.

> With another PRN serving as a modulation source, the variations will not be
> unlimited either. You will get some repetition as well - only much later. It
> would surely be an improovement compared with one single PRN.

Yes.

> The big question is, will this improovement be better than simply investing
> the additional PRN in an increased length of the first one, rather than
> splitting in two PRNs and finding an optimal modulation algorithm ?
> What if for a certain number of flipflops the linear arrangement of all
> flipflops
> *is* the best algorithm ?
> (I cannot answer this.)

Let me try to provide an answer.

Given that we have two PRN sequence machines, A and B. We let A clock the B
machine with it's output. Our output signal is the output of the B machine.

If we consider both the A and B PRNs as being state machines, having a 2^N-1
number of cyclic states property (where N is either NA or NB), we can have at
most

  NA          NB         NA+NB    NA    NB
(2   - 1) * (2   - 1) = 2      - 2   - 2   + 1

states in the combined state machine. However, if we where rigging the two
shift registers as a common PRN setup, then we would have

 NA+NB
2      - 1

states. Thus, regardless of HOW we try to rig PRN A to control the advancement
of PRN B, this would allways be worse, then trying to rig them into a single
PRN. The only way to get around this is to add more statemachines (flip-flops
or whatever), but the comparision is only of interest if we allow as many bits
in the statemachines. Thus, the Maximum Length Sequence is called so since it
has a period which is only one less then the theoretical maximum of that
hardware (state holding).

Note also that one has to select the individual length of the A and B machines
with care, or otherwise they migth have a much shorter looping time than
anticipated.

Regardless of this theoretical proof that you get longer sequences by running
a common PRN rather than two separate, this does not eliminate that there are
other interesting aspects with doing such an exercis, like the power
distribution over the spectra.

Cheers,
Magnus