On Thu, 4 May 2000, Andrew Warren wrote:

> Andrew Kunz <PICLIST@MITVMA.MIT.EDU> wrote:
>
> > I had nothing to do with the algorithm other than coding it.
> >
> > There may have been something about the designer's concept that isn't
> > here, mainly because I didn't need to understand the concept.
>
> Hmm... Maybe adding the digital noise made that pseudo-average
> algorithm converge faster?  I'd have to think about it for a bit;
> maybe Scott Dattalo can answer more quickly.

I can't see how it'd possibly converge more quickly. If you view the average
operation as a low pass filter and assume that the noise is 'white' (that is, it
has energy at all frequencies) then there will be noise present right up to the
filter's cutoff. If you had a sine wave with a frequency close to the filter's
cutoff, you'd notice that the filter would let some of it through. I think the
same would be true here as well. In other words, I think it would take LONGER to
settle. Now the noise is not truely white since its DC component is absent
(presumably - otherwise you're just adding an error to the signal). The reason
this scheme works in the analog domain so well is that 1) the noise is (or
should be) absent of a any DC component 2) the low pass filter bandwidth is so
low that the amount of energy in the noise over that frequency band is
negligible.

>From this observation it's clear to conclude that adding random noise only works
well if the averaging filter or low pass filter has a very low frequency
cutoff. If you were to use this technique to acquire higher bandwidth data like
acoustical data, this technique would reduce the digitization accuracy. However,
if noise is added in a frequency band beyond the frequency at which your signal
resides, you may again apply these concepts. In this case it will become
necessary to over-sample the data, low-pass filter it, and then decimate it to
the sample rate you would have sampled without using this technique.

Perhaps a simpler approach would be to add a known error signal to your analog
signal. This signal could be sine wave or triangle wave with frequency just
outside the frequency of the signal of interest. Satisfy Nyquist for this known
analog signal (by sampling at 2 or 3 times the frequency of the sine or triangle
wave), then digitally subtract it out, and low pass filter the result. The idea
is that +1 -1 = 0, only the addition is analog and the subtraction is digital.
Now, the digitized sine wave subtracted from the sampled signal needs to have
more resolution than just one bit of your A/D converter other wise you wouldn't
benefit from the dithering.

Caveats - of course I've never tried this, but in theory...

Scott