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From: bobw@col.hp.com (Bob Witte)
Newsgroups: sci.electronics
Subject: Re: Re: Re: A question about Nyquist theorm
Message-ID: <38610005@col.hp.com>
Date: 13 Mar 91 03:32:39 GMT
References: <5782@mit-caf.MIT.EDU>
Organization: HP Colorado Springs Division
Lines: 45

>
>In article <605.27c28109@zodiac.rutgers.edu> bittel@zodiac.rutgers.edu writes:
>>I had a professor that loved to explain the sampling theory this way.
>>It is not correct!!!  What does the bandwidth have to do with it???
>>Say you have a signal with frequency components from 5000 to 5100 Hz.
>>The bandwidth is 100 Hz.. Does that mean you can sample at 200 samp/sec and
>>get the signal??? NO!!
>
>YES!!  Your professor was right.  You have to sample for all time, of course,
>but you can get the signal.
>
>That's why you need anti-alias filters, so you get the band you want.  Without
>a filter, all the 100Hz bands you can think of get aliased to the same place.
>0-100 Hz, 5-5.1 KHz, 1-1.0000001 GHz.

  I agree with you here. 

>
>How do you think digital sampling scopes work?  The HP54501A has a 100 MHz
>bandwidth, but samples at only 10 Msamples/sec.  Yes, I know these instruments
>do a lot more than simple sampling, but they do acquire signals faster than
>their sampling rate.  And they do alias, if you're not careful then
>what you see may not be what you got.

  I don't agree here, though. Digital scopes often are designed with a
  low sample rate relative to the bandwidth. Such scopes work only on
  repetitive signals, taking advantage of the fact that the scope gets
  several "passes" at the waveform to acquire the entire signal. Keeping
  track of the time between a particular sample and the trigger event
  allows the scope to put together a good reproduction of the waveform.
  In this case, the waveform is definitely not bandlimited to fs/2,
  otherwise you wouldn't get a 100 MHz bandwidth with a 10 MSa/sec 
  sample rate.

  This is "undersampling" but is distinctly different than the previous
  case.
 
    
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Bob Witte              HP Colorado Springs Division
bobw@col.hp.com        P.O. Box 2197
Phone:(719) 590-3230   Colorado Springs, CO  80901
Radio: KB0CY            
"Of course, then again, I've been wrong before."
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