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From: mcmahan@netcom.COM (Dave Mc Mahan)
Newsgroups: comp.dsp
Subject: Re: Discreet Sampling
Message-ID: <26576@netcom.COM>
Date: 2 Mar 91 22:47:35 GMT
References: <1991Feb28.194203.27097@alzabo.ocunix.on.ca>
Organization: Dave McMahan @ NetCom Services
Lines: 32


 In a previous article, rob@alzabo.ocunix.on.ca (Robert Hilchie) writes:
>It is claimed that any signal sampled at a rate of 2s can be reproduced exactly
>(provided that the original signal did not contain frequencies above s).
>
>Now suppose the sampling rate is 40 kHz and the signal being sampled is a
>sine wave of constant amplitude at 19 999 KHz. At some point the samples will
>occur near the peaks and troughs of the sine wave, while, half a second later,
>the samples will occur at the midpoints between the peaks and troughs. Thus,
>the reproduced signal will fluctuate in amplitude every second.
>
>How can this "beating" be avoided?

It can't be avoided.  What you need after you do your reconstruction is a low
pass filter that can handle your reconstructed waveform.  In the case listed
above, you would need a filter that can pass 19.999 KHz with no attenuation
and would provide 100% attenuation at 20.000 KHz (minus a little bit).  This
kind of filter is sometimes known as a 'brick-wall filter' and usually only
exists on the blackboards of professors who teach about Nyquist and sampling.
In the real world, you have to take your output filter into account when you
develop your sampling system.  Your example above is theoretically quite
correct assuming you use the brickwall filter, in the real world it will be
quite difficult to implement.

>Rob Hilchie
>rob@alzabo.ocunix.on.ca

   -dave

-- 
Dave McMahan                            mcmahan@netcom.com
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