Re: [SI-LIST] : Nyquest Sampling Rate

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From: David Instone (david_instone@uk.xyratex.com)
Date: Mon Apr 02 2001 - 01:57:27 PDT


All,
  I'm glad Adam asked this, the same thing has been bugging me for
years! Of all the answers I guess the one below from Mike made the the
most sense to me.
  Here's what I got from it-
  You actually have to sample at just a bit higher than f*2. How much
higher depends on how long you want to wait before every amplitude point
of the sinewave has been sampled.
  So if I am prepared to wait for an infinite time I can sample at
(f*2)+10E-infinity, and as the difference between f*2 and
(f*2)+10E-infinity is infinitely small I can say I am sampling at f*2.
   Alternatively,,,,, as I know it's a sine wave then once I've taken
four samples at that slightly higher rate then I can reconstruct the
sinewave anyway without having to wait for infinity!
 
  Which makes me wonder if the nyquest rate could actually be called the
lowest rate at which it is just NOT possible to recover the signal.

Dave

Mike Jenkins wrote:
>
> Adam,
>
> It's not two points. It's an infinite sequence of samples T/2
> apart. That is, Nyquist's theorem is about steady state. This
> infinite sequence of evenly spaced samples unambiguously identifies
> a signal if the signal has all components below 1/T in frequency.
>
> Try finding more than one sinewave through the points
> A*sin(2*pi*F*n*T/2) where F < 2/T and n=1,2,3,....
>
> Hope that helps.
>
> Regards,
> Mike
>
> >
> > DEAR SI list subscribers,
> > Can any one explain to me how you can recover a
> > periodic signal form only 2 samples. I can understand
> > the math but I am having difficulty visualizing this.
> > Draw me any 2 points in the time domain and I can make
> > endless number of periodic signal go through them?
> >
> > I know I am missing a key point but I can quite put my
> > finger on it.
> >
> > Your input is very well appreciated.
> >
> > Adam
> --
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Mike Jenkins Phone: 408.433.7901 _____
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> 1525 McCarthy Blvd. mailto:Jenkins@LSIL.com | |
> Milpitas, CA 95035 http://www.lsilogic.com |_____|
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-- 
Regards

Dave Instone. Compliance Engineer Storage Systems Development, MP24/22 Xyratex, Langstone Rd., Havant, Hampshire, P09 1SA, UK. Tel: +44 (0)23-92-496862 (direct line) Fax: +44 (0)23-92-496014 http://www.xyratex.com Tel: +44 (0)23-92-496000

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