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Tue Jul 10 15:40:09 EDT 2012

Analog Synth using Sigma/Delta signals

So the question is: do the calculations on expected values in in [1]
actually make sense?  Due to modulation, part of the spectrum will
probably end up in the base band, but maybe this doesn't show up in
the expected value because the average is invisible?

It's probably best to code up a couple of examples and compute
spectra.  However, it still seems that if the noise is not correlated,
the result should be 0 at DC.  With C = A x B, the spectra are
              _
     C(f) = _/ A (f-x) B(x) dx

It really seems that the trick is non-correlated noise. In the
following
              _
     C(f) = _/ [ A(f-x) + A_n(f-x) ] * [ B(x) + B_n(x) ] dx

the convolution of the noise terms should be zero.
              _
        0 = _/  A_n(f-x) B_n(x) dx

If the bands of A(f) and B(f) are small, the noise band in C(f) will
only grow a little, but it will grow: any non-DC signal A(x) | B(x)
smears out the noise B_n(x) | A_n(x) a little.

So it seems that [1] is sound, given that there is no correlation.

The real question is then: how to decorrelate S/D streams?

[1] entry://20090609-111303



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