[SI-LIST] Re: Square wave harmonics
- From: Michael Nudelman <mnudelman@xxxxxxxxxxx>
- To: "'doug@xxxxxxxxxx'" <doug@xxxxxxxxxx>, lucien_op@xxxxxxxxx,si-list@xxxxxxxxxxxxx
- Date: Mon, 26 Nov 2001 17:34:33 -0500
>>>The rest of you working guys ....
Is this how we are referred to from now on?
-----Original Message-----
From: Doug Brooks [mailto:doug@xxxxxxxxxx]
Sent: Monday, November 26, 2001 5:35 PM
To: lucien_op@xxxxxxxxx; si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: Square wave harmonics
Perhaps the simplest way to view this is to imagine the following
experiment. "Drive" a line with a square wave. Place a tuned filter on the
line to "pick off" specific frequencies. If the square wave "consists" of
specific harmonics, the harmonics will respond, or pass through, the filter
when the filter is tuned to each specific harmonic frequency. You will find
that, in fact, the specific harmonics will pass through.
The simplest way to "build" a square wave (at least in concept) is to flip
a switch rapidly. That's got nothing to do with sine waves! But square
waves do not appear naturally in nature; sines and cosines do. The natural
waveforms that combine to make the square wave are found with the Fourier
Series.
Since you are a graduate student, I will send you (under a separate e-mail)
a complimentary copy of UltraCAD's square wave simulator so you can play
with it and look at the various variations. (The rest of you working guys
will have to buy the book! See below). Perhaps that will help clarify
things.
Doug Brooks
UltraCAD
At 09:59 PM 11/26/2001 +0000, lucien_op@xxxxxxxxx wrote:
>I'm an undergrad at UW, Seattle. I have a question concerning square
>waves.
>
>My signals text book says, a square wave is modeled by a sum of
>harmonically-related sinusoids (the Fourier series). Mark the word
>"modeled." Another source uses the term "represented."
>
>Recently, I've been told at my workplace by several senior
>engineers that a physical square wave is PHYSICALLY composed of
>harmonics. In other words, they say that the Fourier series is not
>just a mathematical tool describing square waves, but is indeed an
>accurate description of the physical square wave. They tell me all
>physical square waves contain harmonics.
>
>The two ideas above seem in conflict. My undergraduate brain is
>growing frustrated, and all I can conclude with certainty is that a
>square wave BEHAVES AS a Fourier series, regardless of how it is
>created.
>
>I know from reading HP manuals for signal/pulse generators that these
>devices do not build square waves by adding sinusoids. So in my mind,
>it doesn't seem possible that these square waves can contain
>harmonics. As for how a spectrum analyzer gives Fourier Coefficients
>I have no idea. I don't know if it just calculates and displays the
>Fourier coefficients, or if it actually detects physical harmonics
>within a signal and displays their magnitudes.
>
>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?
>
>
>Lucien Opperman
>Seattle
>
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***********************************************************
Doug Brooks' book, "Electrical Engineering for the Non-Degreed Engineer is
now in its 3rd printing. Learn about it at www.ultracad.com
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