[linux-audio-dev] Direct Stream Digital / Pulse Density Modulation musing/questions

[Alfons Adriaensen]

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