17 Jun
2005
17 Jun
'05
6:39 a.m.
On Sat, Jun 11, 2005 at 09:46:23PM +0200, Mickael Vardo wrote:
Just try this "simple" experience: sample a
1 Hz pulse that
is triggered after a random non-quantized delay that is less
than four seconds. Sample it at a rate of 2 sps and then,
try to get the original signal back with all its components
(phase and frequency). Good luck.
Of course this will not work. A 1 Hz pulse has energy well
above 1 Hz. If you sample it at 2 sps, information is lost.
This is just as impossible as saying that you can
compress the
information stored in any analog signal in a finite number
of samples.
If the bandwidth of the signal is finite, a finite number of
samples per time is always sufficient to contain all the
information. If this were not true, then a finite bandwidth
signal with a finite S/N ratio would be able to carry an
infinite amount of information. If you find a way to do that
you will redefine the telecom industry and be rich and famous.
In the process, you'll have to rewrite most of mathematics as
well.
--
FA