Klarinet Archive - Posting 000717.txt from 1997/11

From: "Jerry Korten" <jerryk@-----.com>
Subj: Re: Nyquist
Date: Thu, 20 Nov 1997 11:18:11 -0500

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
>

This is the issue I was hung up on, the Nyquist theorem as stated on the
list is missing the part about reconstruction. The digitized waveform does
look nothing like the sampled waveform. However upon reconstruction (using
a filter function to interpolate the values) you can get back the original
waveform... If an A/D is not used in the process. If an A/D is used the
quantization effects will not allow us to perfectly reconstruct the
waveform.

Jerry Korten
NYC