On Wed, 3 May 2000, James Newton wrote:

> <BLOCKQUOTE AUTHOR="Alice">This refers to GRAPHING the numbers</BLOCKQUOTE>
>
> <BLOCKQUOTE AUTHOR="Andy">Xunknown + Noise = Xreal (more closely,
> anyway)</BLOCKQUOTE>
>
> Ok, kids. Which is it? <GRIN>
>
> Specifically, I understand Alice's point but is Andy talking about averaging
> data or what? How else can an Xunknown be made more Xreal with noise?
>
> Also, doesn't adding a "third dimension to the graph" have the same effect
> as averaging during the time that the Xunknown is at that point? in that it
> makes it clear that X was REALLY at this point for a while.
>

I believe that what they're saying is that at long as your A2D converter has
fairly stable transitions that you can add 'noise' to the signal, then you can
filter the noisy signal obtain a more accurate representation of the 'real'
signal. You can imagine a similar effect without noise. Suppose you have at your
disposal a saw-tooth wave form that varies in amplitude by an amount equal to
say one count of your A/D converter. Now further suppose that your able to
precisely add this to your unknown signal. If you poll the A/D converter while
you apply the triangle wave and measure how long it takes for the A/D converter
to increment, you can calculate how far between the quantized voltages that your
signal is.

This is wonderful in theory, but in practice it ain't so easy. For one, the
signal under test varies. You could add an additional sample and hold circuit in
front of the A/D but why add the cost (and [uncontrolled] noise)? However, if
you add a controlled noise source to the signal you can achieve the same
results as you can with the theoretically perfect saw tooth waveform. The idea
is that the random noise will cause the signal to bounce around and cross
several of the quantized voltage levels. The only thing you need to do is low
pass filter (i.e. average) the consecutive samples to achieve the more accurate
reading.

I can imagine a simple example where the controlled noise varies by 2 A/D
counts. If you measured your signal without the noise you'll get a count of
X. If you add the noise, your signal will vary between X-1, X, and X+1. If more
readings were obtained in the X+1 bin than the X-1 bin, then you can say that
the original 'X' value is between X+0.5 and X+1. This is essentially one more
bit of information. And certainly a longer average over many samples will
improve the estimate. (But you'll still need to take into account your varying
signals...)

Scott