Klarinet Archive - Posting 000704.txt from 1997/11

From: Ian Dilley <imd@-----.uk>
Subj: RE: Nyquist and analog
Date: Thu, 20 Nov 1997 06:46:39 -0500

The likelihood of this occurring in a real situation is irrelevant here.
I was just pointing what seems to me an obvious case where this theorem,
as stated, fails.

-----Original Message-----
From: Roger Shilcock
[SMTP:roger.shilcock@-----.uk]
Sent: Thursday, November 20, 1997 8:43 AM
To: 'klarinet@-----.us'
Subject: RE: Nyquist and analog

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

On Wed, 19 Nov 1997, Ian Dilley wrote:

> Date: Wed, 19 Nov 1997 17:12:44 -0000
> From: Ian Dilley <imd@-----.uk>
> Reply-To: klarinet@-----.us
> To: "'klarinet@-----.us'"
<klarinet@-----.us>
> Subject: RE: Nyquist and analog
>
> Here is the disputed definition of Nyquist's theorom
>
> Nyquist's theorem: A theorem, developed by H. Nyquist, which
states that
> an analog signal waveform may be uniquely reconstructed,
without error,
> from samples taken at equal time intervals. The sampling rate
must be
> equal to, or greater than, twice the highest frequency
component in the
> analog signal. Synonym sampling theorem.
>
> Well, I'm no expert but I can immediately see a case where
this is not
> going to be true. Take as an example a 20 KHz sine wave
sampled at 40
> KHz. According to the above definition the samples will
contain enough
> information to perfectly reconstruct the 20 KHz sine wave.
>
> Surely you are going to get different results depending on the
relative
> phases of the sampling and the sine wave itself. In one
extreme case
> you could get a set of samples that are all 0. This occurs
because the
> wave crosses the 0 point every 1/2 it's period. From that you
aren't
> going to be able to reconstruct very much at all! At the
other extreme
> you can get a series of +n, -n, +n, -n ... where n is the
amplitude of
> the signal.
>
> Jerry, Jonathon - am I missing something obvious?
>
> Ian Dilley
>