"SolarFlare" wrote in message
...
Now you have to provide samples ***AND*** changing
information with an algorthm to decode successfully.
Your samples are then not complete and useless without
other information supplied.

This is true, but it's pretty much true for all communication systems, not
just sub-sampled digital ones. What changes is that sometimes the extra
'information' supplied can be done by something as sophisticated as a human's
brain as he tunes across the dial to find the 'best' sound -- this
corresponding to finding the carrier. (At some point this becomes a very
philosophical discussion... 'information' only has _meaning_ to an observer
who presumably knows something about or has a hunch as to what they're
observing is. Although one can compute the 'information' within signal in an
attempt to ascertain whether it resembles a random process or whether it's
conveying what we may 'intelligence.' Hence you can probably recognize the
difference between someone speaking random jibberish and an actual language
even without knowing that language, but on the other hand a good way to
conceal information is to make it appear almost completely random -- when in
fact it isn't --, which is exactly what cryptography does.)

Let's see you regenerate the original carrier and
information from that without the carrier frequency
known.

Example: Take an antenna that's about a meter long... feed its output to an
LNA and then a reasonably steep bandpass filter passing 144-148MHz... sample
with a 16 bit, 12MSps ADC (I chose 12 just because it shifts 144MHz to
baseband, although there's no reason you can't use any frequency 8Msps).
Feed this digital word to a 16 bit DAC clocked at 10MSps. Lowpass filter the
DAC's output with a reasonably steep 4MHz low-pass filter. Feed this signal
to one port of a mixer and 144MHz to the other port. Poof! There's your
original signal back again! Feed this through another 144-148MHz bandpass
filter if you don't like the image response at 140-144MHz.

There are a few caveats he

1) Clock jitter will tend to broaden out the specctra of the original signals
a bit (how good is your clock?)
2) The track & hold (analog) circuitry in the ADC has to be good to a couple
hundred MHz to avoid distortion.
3) Your noise floor is limited to no better than ~-100dB (and potentially
_much_ worse if you haven't been careful in your layout, power supply
decoupling, etc.). Note that everything described above also applies to
switched capacitor circuits (a technology whose time has just about passed,
but a neat idea); in that case analog noise rather than quantization noise
will dictate the noise floor (and realistically it'll probably be much worse
than -100dB...)
4) A typical DAC holds its output (e.g., a first-order hold) rather than
generating impulses, so the spectrum reproduced has a sin(x)/x profile to it
(frequencies closer to 148MHz will have less gain than those at 144MHz); this
can be fixed in the digital domain with the use of a FIR or IIR filter. In
some systems the droop is small enough that people just ignore it.

This example is reasonably practical. Strictly speaking, to make it simlper
you can just bandpass filter the output of the DAC directly and be OK, but the
sin(x) profile along with the limited analog bandwidth of the DAC tend to make
this approach impractical (you end up with very little SNR); this approach if
often used for proof-of-concept demos, though.

If you happen to have a carrier at 146.23MHz in the input signal, it'll most
certainly still be there in the output signal, yet the system didn't have to
'know' where the carrier was.

When you listen to the audio on your radio can you tell
the carrier frequency without the dial?

Sure, I can measure it! In fact, a much more interesting problem is how one
generates a carrier when none exists in the first place. There are plenty of
modulation schemes out there specifically don't use a carrier to either save
power (TV transmissions -- which have a very small albeit not eliminated
carrier -- are a good example of this) or to conceal transmissions (in
military systems nothing attracts unwanted attention more than a carrier some
60dB above the noise floor).

---Joel