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Which is why the Nyquist sampling constraint does not assume a sinusoid,
nor is it expressed in terms of the fundamental. It is properly
expressed in terms of the bandwidth (and not the 3dB bandwidth, nor in
terms of the maximum frequency). With a squarewave, even 10x can be
insufficient. And with impulses, it's even worse. The Nyquist criterion
is really quite straightforward. It's just that many have never bothered
to read what Nyquist actually said.

The sinewave example I gave is an example of "lies we tell to children"
to avoid the maths. When I follow that up with a lecture using the
proper maths, I point out that a sine occupies zero bandwidth, so
Nyquist actually tells us that we could sample it at an arbitrarily low
rate without losing any information at all, because a sinewave actually
has no information. Then that leads to a revisiting of aliasing,
sampling scopes, and compressed sensing, and also sets us up for an
extended discussion on Shannon channel capacity.

-- Cheers
Tom

--
Prof. Thomas H. Lee
Allen Ctr., Rm. 205
350 Jane Stanford Way
Stanford University
Stanford, CA 94305-4070


On 11/22/2021 13:15, David C. Partridge wrote:

Any assumption that you are looking at a sine wave is frankly na?ve.

From experience if you are using a DSO that's sampling at under 10x the

fundamental frequency of a signal (e.g. 1GHz square wave sampled 5Gs/s),
then you are doomed to get an inaccurate signal representation.

David

-----Original Message-----
From: [email protected] <[email protected]> On Behalf Of Tom Lee
Sent: 22 November 2021 19:31
To: [email protected]
Subject: Re: [TekScopes] bandwidth

Steve,

I'm sorry to advise the others here to disregard your post. You have
made several profound misstatements here and elsewhere. If memory
serves, you once posted (maybe on HP groups.io) similar assertions. One
example you gave in support of your position was that of a sinewave
being sampled at slightly above the Nyquist rate, and you incorrectly
claimed there that the reconstruction had amplitude modulation. That
shows that you do not understand the role of the sinc interpolation
function. Properly applied, no such modulation results, and one obtains
perfect reconstruction. It's easier to see that from the frequency

domain.

If you wish to debate this, please do so off list to limit the thread
derail.

-- Tom