Werner,

At the risk of beating the horse to death, I should add to my previous
response that you can actually add essentially any waveform you like
to improve the resolution of the A/D.  For example, you could add a
sine wave instead of a triangular wave.  The only difference is that
the proportions of digital outputs that land in the upper state and in
the lower state will be weighted by the proportion of the time that
the added signal tends to spend at each amplitude level.  For
instance, a sine wave spends relatively more time near its maximum and
minimum values and this must be taken into account in deciding what
weight to place on the proportion of digital outputs found in the
upper level and the lower level.  The reason for preferring a
triangular or saw-tooth (ramp) waveform is simply that these signals
spend equal amounts of time at each amplitude level, so that no
further consideration need be given to the weights to be assigned to
the proportions of the digital outputs in the two output states.

In fact, you can even add an analog random signal.  I.e., garden
variety random analog noise. The amplitude of such a signal is usually
Gaussian distributed.  You only have to take this into account, in the
same way you would the relative amplitude distribution of a sine wave,
in deciding how to weight the proportions of digital outputs you get
in the two states to infer the "true" interpolated input signal level.

A famous example that is closely related to this is the so-called Van
Vleck clipping correction. Here, a random signal is hard-limited to
just two states.  Effectively, it is sampled with the worst possible
A/D, a 1-bit A/D.  Yet, information is ultimately derived as it would
pertain to the signal had it been known to indefinite precision.  That
is, left in its original analog form.  The basis for the trick (the
Van Vleck clipping correction) is nothing more than taking into
account the relative amount of time that the original random signal
amplitude (again, Gaussian distributed) spends at each level and
deducing the corresponding relative proportions of the hard-limited
samples that end up "0" and "1".

Regards,
--- Warren Davis
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