Klarinet Archive - Posting 000726.txt from 1997/11

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

-----Original Message-----
From: Jerry Korten [SMTP:jerryk@-----.com]
Sent: Thursday, November 20, 1997 4:18 PM
To: klarinet@-----.us
Subject: Re: Nyquist

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

I assume that you mean D/A in the above response. I don't
understand what you mean by reconstructing the waveform without using a
D/A converter. Surely anything which converts a digital stream to an
analog stream is by definition a D/A converter.