[sdiy] Analysis of frequency variation in analogue synths

[Magnus Danielson]

From: Eric Brombaugh <ebrombaugh at earthlink.net>
Subject: Re: [sdiy] Analysis of frequency variation in analogue synths
Date: Sun, 06 May 2007 14:30:04 -0700
Message-ID: <463E48DC.4000602 at earthlink.net>

> ASSI wrote:
> > On Freitag, 4. Mai 2007 23:42, Tom Wiltshire wrote:
> >> This is a 32-bit shift register noise generator producing 8-bit
> >> values, which are then fed into a simple averaging filter.
> > 
> > If you take more than a single bit per cycle out of an LFSR, then those 
> > bits are highly correlated in time.  This transfers to the words you 
> > build from those bits and the correlation creeps into the averaging you 
> > perform as well.
> 
> True. What will that correlation look like on the output of the 
> averager/filter?

They are correlated with only a time-shift inbetween. Xor any of the bits
together and you get another shifted variant. It's nothing but linear filtering
in the Galois field and any taps and xoring of taps results in phase-shifts.

> Given that the LFSR is 32-bits, how narrow would the 
> filter have to be (how many cycles) before the effects of the 
> correlation are negligible?

They always correlate. Hevily.

> I'd think anything > 32 cycles would approximate the same results you'd get
> by just clocking the LFSR 32x faster. Also, what would be the effects of
> scrambling the LFSR bits when forming the output word?

Scrambling one stream with another from either a different rate or different
code will get you a different longer code.

> It's probably worth throwing together a few Matlab simulations to 
> investigate. Are you aware of any publicly available papers on the subject?

There are always papers, what do you specifically want a paper on?

Cheers,
Magnus