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From: ingoldsb@ctycal.UUCP (Terry Ingoldsby)
Newsgroups: sci.electronics,comp.dsp
Subject: Re: A question about the Nyquist theorm
Summary: More questions about practical sampling
Message-ID: <625@ctycal.UUCP>
Date: 26 Feb 91 00:18:04 GMT
References: <20408@shlump.nac.dec.com>
Organization: The City of Calgary, Ab
Lines: 50

Pursuing the discussion of the Nyquist theorem, I have a question
about practical sampling applications.  If you have a sine wave at
frequency f, which you sample at just over 2f samples per second then
the Nyquist theorem is satisfied.  I know that by performing a Fourier
transform it is possible to recover all of the signal, i.e. deduce that
the original wave was at frequency f.

Note that this is different than just playing connect the dots with the
samples.  Most of the algorithms I've heard of used with CD players
perform a variety of interpolation, oversampling, etc., but these all
seem to be elaborate versions of connect the dots.  I'm not aware that
the digital signal processing customarily done will restore the wave to
anything resembling its original.

I suspect that there is something I am missing here.  Can anyone clarify
the situation?

E.g.

Original:


      x x         x x         x x
     x   x       x   x       x   x
    x     x     x     x     x     x
           x   x       x   x       x
            x x         x x

    ^    ^    ^    ^    ^    ^    ^
Sample points 


Connect the dots reproduction (you can draw in the lines, I hate ascii drawings)

                   x
         x    
    x
              x              x    x
                        x

The only thing I can think is that the resulting waveform must contain
frequencies greater than the Nyquist limit allows, thus permitting them
to be filtered out with a brick wall filter (approachable with digital
filtering) letting the orignal come through unaltered.  Can someone confirm
my belief?

-- 
  Terry Ingoldsby                ingoldsb%ctycal@cpsc.ucalgary.ca
  Land Information Services                 or
  The City of Calgary       ...{alberta,ubc-cs,utai}!calgary!ctycal!ingoldsb