Klarinet Archive - Posting 000727.txt from 1997/11

From: Ian Dilley <imd@-----.uk>
Subj: RE: Nyquist and analog
Date: Thu, 20 Nov 1997 11:18:21 -0500

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

Ian Dilley

-----Original Message-----
From: Jonathan Cohler [SMTP:cohler@-----.net]
Sent: Thursday, November 20, 1997 1:26 PM
To: klarinet@-----.us
Subject: RE: Nyquist and analog

>No doubt this shows that "greater than" is better than "equal".

In real life, everyone samples at greater than 2F, for technical
reasons.

But the theory is correct at 2F. As I said in another message,
the
probability of your sampling device precisely obtaining all the
zero
crossings, is precisely 0 and therefore not an issue. An
interesting
anomaly to discuss, but not an issue.

> Ian's
>point looks valid, but is it likely, in a real situation, that
the
>sampling rate is going to be exactly in phase with one (or
more)
>components? Furthermore, nobody is sampling components - what
is being
>sampled is a *resultant* waveform.

Exactly.

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