Discrete Data frequences

Can any explain why discrete data can only contain frequencies between
DC and one-half the sampling rate?

Many Thanks

in article 436801c2.0503051031.12dd374a@posting.google.com, blix at
bavarianbista@hotmail.com wrote on 03/05/2005 13:31:

> Can any explain why discrete data can only contain frequencies between
> DC and one-half the sampling rate?

it's not that it *only* contains those frequencies, but that the spectrum
repeats itself forever at every integer of the sampling rate.  this is a
fundamental property of sampled signals from the
Nyquist/Shannon/Whittaker/Kotel'nikov Sampling and Reconstruction Theorem.
(is there anyone else to credit for it.)  to see my spin on it see

http://groups-beta.google.com/group/comp.dsp/msg/f9e0ad7b430bc653?fwc=1

but ignore all of the bullshit from Airy R. Bean.

if you can't read the ASCII math in that post, i have a variant in a PDF doc
that i can send you or anyone else who wants one.  if you don't get the math
in it, then i would say there is a prerequisite issue.

--


r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

blix wrote:
> Can any explain why discrete data can only contain frequencies between
> DC and one-half the sampling rate?
> 
> Many Thanks

Consider a set of samples 1,1,1,1,... That can come from scanning DC, a 
pure tone at the sampling frequency, at double the sampling frequency, 
triple the sampling frequency, and so on.

Consider another set 1,-1,1,1-,... That can come from scanning a tone at 
1/2 the sampling frequency, 3/2, 5/2, and so on.

With some thought you can see that a tone a little less than half the 
sampling frequency and one the same amount more can produce exactly the 
same sample train. So just as a particular arctangent can represent many 
angles, a particular sample train can represent many waveforms. You can 
think of those frequencies less than half the sampling frequency as the 
"principle values". Most of the time we restrict ourselves to them. 
There are circumstances when we don't have to if we're very careful.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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