[sdiy] Long LFSRs (Was Psych Tone)

[ASSI]

On Sunday, January 6, 2019 11:09:26 PM CET Bernard Arthur Hutchins, Jr wrote:
> In response to the recent discussion of the classic “Psych Tone”, here I
> have added three items (from MEH, EN64, EN75A):
> 
> http://electronotes.netfirms.com/Noise.pdf
> 
> 
> 
> adding to the Electronotes 76 already posted on noise generators:
> 
> http://electronotes.netfirms.com/EN76.pdf

Wonderful, thank you!

> The MEH chapter 5h pages include the reference to the derivation of the
> feedback taps based on “primitive polynomials”.  Since EXOR feedback is
> anything but “linear”, I don’t understand the terminology “LFSR”, and
> continue to use “PRBS” (pseudo random binary sequence).

An EXOR is simply multiplication (given the right encoding).  That is what 
allows an LFSR to implement a matrix multiplication with such low hardware 
complexity.

[…]
> It doesn’t help enough to find a set of taps with one
> nearly at the input end.  What does work is to have TWO (or more) PRBS
> generators of different lengths and multiplying (EXOR) the outputs.

Yes.  That works because whatever the original distribution(s), mixing them 
will (rather quickly under easily met conditions) converge towards a Gaussian 
one (says the central limit theorem).


Regards,
Achim.
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