Tue Jul 3 08:41:27 EDT 2012

Mixers and integrators

Maybe it's time to try the Sigma/Delta synth again, using two building

 - the integrator = counter + S/D converter

 - the mixer = "random" bit stream multiplexer

Where "random" means the switch waveform is not corrlated with the S/D
"waveform".  It would probably be enough to make it into a cheap LFSR.

Before doing this on chip, it's probably a good idea to simulate it
first in Haskell.  After that it might be interesting to put it in an
FPGA, or a low-frequency version in a PIC.

Theoretically, it would be interesting to find a measure of how
inefficient this actually is.  The main tradeof is to use a use
spectrum so it has an 1/f characteristic, and simplify the "mixer" to
a multiplexer (assuming RNG is free).

Why is an S/D dac/adc beneficial?  It seems that it trades off speed
vs. size, but not in a very efficient way.  However, "speed is free".
HW runs in MHz/GHz range, about 1000x more than ordinary audio
sampling frequencies.  Apart from time-multiplexing (i.e. sequential
computer programs) there is no way to easily use these extra cycles.

One thing I don't really understand is how to look at "information".
It's said that the higher bands contain noise, but that's not really
true.. it's because of the "noise" in the higher bands that the
information in the lower bands can fit in the 1-bit dynamic range.  It
doesn't seem that these higher bands can actually contain information
along side the low band signal.  However, the encoding is very robust
against random bit errors: they definitely introduce unwanted signals,
but they do it in a gracefully degrading way.

It would be interesting to compute the theoretical capacity[4] of a
channel with the same noise envelope as a s/d and see how it relates
to the digital bit rate.

Not to forget, for signals close to the 0/1 voltage, a S/D acts as a
voltage <-> frequency converter.  Closer to 1/2 voltage this is the
same, only modulated near to 1/2 the output frequency.  In this mode
is is clear that DC accuracy is actually infinite (infinite
integration time) so to talk about "dynamic range" is always dependent
on frequency.

[1] entry://20090609-145519
[2] entry://20101227-110515
[3] entry://20100218-104438
[4] http://en.wikipedia.org/wiki/Channel_capacity