Klarinet Archive - Posting 000745.txt from 1997/11

From: Jonathan Cohler <cohler@-----.net>
Subj: RE: Nyquist and analog
Date: Thu, 20 Nov 1997 13:44:41 -0500

Ian Dilley wrote:

>I realise that the situation I described would not be an issue in
>practice. I was just questioning the definition of Nyquist's theorem.
>
>I don't understand why you say that the probability of obtaining all 0
>crossings is precisely 0. There is an infinitely large set of possible
>sets of samples and the probability of obtaining any one is the same as
>any other. Therefore, if the probability of getting all 0 crossings is
>0 then the probability of getting any set of samples must also be 0.

That is correct. In other words, the probability of landing precisely on a
particular number when you sample a signal is precisely 0, because there
are an infinite number of numbers that you could land on and you have
selected only 1. The probability is 1 divided by infinity (in simple
terms) or 0.

>This is obviously not true so the probability of getting all 0 crossings
>cannot be 0.

See above.

------------------
Jonathan Cohler
cohler@-----.net