Xref: utzoo sci.electronics:18149 comp.dsp:1326
Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!wuarchive!zaphod.mps.ohio-state.edu!pacific.mps.ohio-state.edu!linac!att!pacbell.com!tandem!netcom!mcmahan
From: mcmahan@netcom.COM (Dave Mc Mahan)
Newsgroups: sci.electronics,comp.dsp
Subject: Re: A question about the Nyquist theorm
Message-ID: <26574@netcom.COM>
Date: 2 Mar 91 22:35:15 GMT
References: <625@ctycal.UUCP> <11515@pasteur.Berkeley.EDU> <1991Feb28.084837.7506@appmag.com>
Organization: Dave McMahan @ NetCom Services
Lines: 40


 In a previous article, appmag!todd@hub.ucsb.edu writes:
>Not all CD players just insert zeroes.  I used the same double oversampling
>chip and the same DAC as my Denon 1500 CD player (well, I used the serial
>versions) in my 56000 project board.  The oversampling chip did do
>interpolation (and it was slightly more complex than bilinear (cubic spline?
>I don't remember)).
>
>I know the math works for inserting zeroes if you use a sinc function to
>reconstruct the signal.  However, how does it work out for reconstruction
>with a near step function?  I've never run through the math on that one...
>Quickly off the top of my head, it doesn't look like it will work...

Weell, If you look at the frequency content of a step function, you will find
that it contains harmonics that stretch into infinity.  To get a perfect
representation of that function when you re-construct, you would need
samples that are spaced infintly close together.  Since this can't be done
(without actually using the original function, since it is the only
representation of this type of sampling that meets the Nyquist criteria),
you can never re-construct the original step.  If you wish to sample this
function and then re-construct it, you will first need to lowpass filter it
to get rid of all harmonics greater than 1/2 your sample frequency.  This
will instantly transmute your nice step function into something resembling it
but containing overshoot and/or ringing right at the step edge.  You can
re-construct THAT waveform exactly, but it's not going to be a perfect step.

Vertical edges get lost during sampling.  A close representation will be
generated during reconstruction, but you will never get the perfect step
(or squarewave) that you originally had.


>Todd Day  |  todd@appmag.com  |  appmag!todd@hub.ucsb.edu


   -dave


-- 
Dave McMahan                            mcmahan@netcom.com
					{apple,amdahl,claris}!netcom!mcmahan