SolarFlare wrote:

OK let's go with your analogy example of 1234 being
represnted by 234 only.

You have no way of decoding 234 into 1234 without
passing information of 1000 as your baseband info and
therefore the the number 1234 has not been successfuly
representedm as being reproduced without further
information.

Now we could further argue algorythms as part of the
information or part of the sample.



Likewise, you have no way of discerning 234 is actually 234 and not 1234
with a 3 digit decimal number system. The problem is not unique to
sub-sampling, it exists at baseband as well. The only difference is
that at baseband the representation looks the same as the signal. In
either case, you need to know the fixed constraints of the system to
fully comprehend the meaning of the representation. For example, in a 3
decimal digit system, you have no way of knowing that 234 really is 234
and not 1234 or 2234 unless you also know that the inputs are limited to
the range 0 to 999. The only way around that is to have an infinite
number of "symbols" to represent all the possible data when the set of
possible data is infinite. As soon as that set is not infinite, we can
take advantage of our knowledge of the system to reduce the set of
symbols to a manageable number of elements. I'd argue that any
engineering requires a set of implied constraints in order to make the
problem solvable.

In the case of the subsampling, we know by design what the pass-band of
the anti-alias filter is. That is a constant parameter designed into
the system, so presumably it is know to designers of all the components
of the system.

In the example case, then, we set as a system constraint the fact that
all inputs are in the range of 1000 to 1234. That constraint is a
constant, and is implied by the design. No information is lost by not
transmitting the constant that is already known throughout the system.
Doing so simply wastes bandwidth on your communications channel.