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From: jgk@osc.COM (Joe Keane)
Newsgroups: sci.electronics
Subject: Re: Re: A question about Nyquist theorm
Summary: Bandwidth is key.
Keywords: sampling, bandwidth
Message-ID: <4573@osc.COM>
Date: 26 Feb 91 21:11:18 GMT
References: <1991Feb17.115102.15399@Neon.Stanford.EDU> <605.27c28109@zodiac.rutgers.edu> <5782@mit-caf.MIT.EDU> <7WB-9MC@irie.ais.org>
Reply-To: jgk@osc.COM (Joe Keane)
Organization: Versant Object Technology, Menlo Park, CA
Lines: 29

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, you can.  The signal you mention is close to periodic.  It can be
considered as a 5050 Hz sine wave modulated by some signal with no components
at frequencies greater than 50 Hz.

If you look at a short segment of the waveform, it's going to look like
something between a 5000 Hz sine wave and a 5010 Hz sine wave.  There's no
point in sampling enough to get the shape of the waveform, because we already
know what it's going to look like.  You just need to sample enough to
determine the modulating signal.

Actually there is one frequency (5000 Hz) where we are missing one of the
components, since it is a multiple of the sampling frequency.  As mentioned
before, this is just a problem with the method of sampling.  It can be
eliminated by shifting the signal up or down a bit in frequency, or using
other sampling methods.

This is the reason the sampling scopes mentioned before can work.  If the
shape of a waveform is not changing rapidly, it only takes up a small amount
of bandwidth.  In other words, you don't need much information to describe it.
There are components at the fundamental frequency and harmonics, but they
occupy narrow bands.  The width of the bands is proportional to the speed at
which the waveform is changing.