SolarFlare wrote:

If only the baseband frequency is sampled at 6kHz then
information is missing to recreate the original 100kHz
and the sampling information is insufficient to
recreate the original signal.


This is analogous to saying the number 1234 can be
represented by
(1234-234) / 1000 = 1

If I supply the number 1.0 you can regenerate the
number 1234 from it? Not true, without the rest of the
sampling information. The sample is incomplete.

Bandwidth sampling only cannot recreate the original
signal.


You've used the wrong part of 1234 for your example. The proper analogy
would be to say that 1234 can be represented by 234 in a 3 digit decimal
number system. In that case, the overflow caused by exceeding 999
results in 1234 aliasing onto 234. If you know that all your input
numbers are between 1000 and 1999, then 234 is sufficient information to
represent 1234 with no ambiguity.

The anti-alias filter on your sampling system performs the bracketing to
make sure that all the possible inputs are constrained to be within a
bandwidth of your center frequency +/- BW/2, so when sampled there is no
aliasing. In essence, that filter is the constraint that makes it work.

BTW, the same holds true for baseband sampling: The numbers in a
baseband system based on your example are assumed to be less than 1000,
so that 234 accurately represents 234. In that case if you put in 1234,
it would also map to 234 and you'd have an ambiguity. It just so
happens that in the baseband case, the representation is the same as the
original signal for signals within the bandwidth allowed by Fs/2. With
other than baseband, the representation is not the same as the number
represented, but the constraints imposed by the system allow you to
reconstruct the original value without ambiguity.