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