[SI-LIST] Re: Square wave harmonics
- From: Michael Nudelman <mnudelman@xxxxxxxxxxx>
- To: "'lucien_op@xxxxxxxxx'" <lucien_op@xxxxxxxxx>,si-list@xxxxxxxxxxxxx
- Date: Mon, 26 Nov 2001 17:17:59 -0500
Lucien:
The answer to your question is rather philosophical one: can you say, that
light consist of particles? Or Waves? Or it is described as waves?
The thing is: in physics there is NO DIFFERENCE between "consist" or
"behave" or "represented".
I will explain: if you create a squarewave by switching two levels of
voltages, or by mixing appropriate sinewaves (let's say, ideal case,
measurably "infinite" number of harmonics), you WON"T be able to tell the
difference.
And when the wave will arrive to the receiver, you won't be able to tell HOW
it was created. Hence - no difference between how you create your squarewave
as long as it is a clean one.
Basically, this is what's good about modeling and measurement: if you use
analogue machine to create just about any function, on the output there is
no difference between modeled function and the real one, since the real
measured function gives you out a voltage, described by function, and the
modelled one gives you exactly the same: voltage described by the same
function.
Being just a receiver of this voltage you won't be able to tell the
difference.
So, it does not matter.
Then again, if you take spectrum analyzer, and will watch teh sepctrum of a
squarewave, you'll find out, that it does actually "contain" all the
harmonics, because you will see them, and, using appropriate filters, may
separate them and make sure they ARE harmonics, described by Fourier
analysis.
Mike.
-----Original Message-----
From: lucien_op@xxxxxxxxx [mailto:lucien_op@xxxxxxxxx]
Sent: Monday, November 26, 2001 5:00 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Square wave harmonics
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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