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On Thu, 4 May 2000, Andrew Warren wrote:

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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

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