[SI-LIST] Re: Square wave harmonics
- From: Steve Corey <steve@xxxxxxxxxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Mon, 26 Nov 2001 20:01:03 -0800
> And also on the other hand, I would assume that the Fourier
> sum is actually limit process, the true square wave being the
> limit of the asymptote. As such, the Fourier can't be looked
> upon as a "real" thing.
Doug:
Agreed, but neither is the "true" square wave to which you refer a
"real" thing. It is defined in the time domain as a limit as well --
both its infinitesimal risetime, and its periodicity defined over an
infinite time interval. And if it did exist, we couldn't measure even
one period precisely...
All this to say, Fourier analysis is based on precise mathematical
definitions, which precision is not available to us in the measurement
world. In both the time and frequency domains, we are left to guess as
to what lies in between the measurement samples, or outside the
measurement window. However, measurable signals contain measurable
Fourier components, to within the precision with which we are able to
measure either one. I think this is basically what you stated in your post.
To the mathematician, measurement of Fourier components is irrelevant in
proving their existence. To the scientist, it implies existence until a
better hypothesis comes along. To the engineer, it means food on the
table next month.
-- Steve
-------------------------------------------
Steven D. Corey, Ph.D.
Time Domain Analysis Systems, Inc.
"The Interconnect Modeling Company."
http://www.tdasystems.com
email: steve@xxxxxxxxxxxxxx
phone: (503) 246-2272
fax: (503) 246-2282
-------------------------------------------
Doug McKean wrote:
> Lucien wrote:
>
>>Can anyone give me the low-down on square waves! Basically, my
>>question is: In our physical reality, do square waves contain
>>harmonics? Or does the idea of square wave harmonics only exist on
>>paper as a mathematical model, used to PREDICT the natural behavior
>>of the square wave?
>>
>
> And also on the other hand, I would assume that the Fourier
> sum is actually limit process, the true square wave being the
> limit of the asymptote. As such, the Fourier can't be looked
> upon as a "real" thing.
--
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