[SI-LIST] Re: Square wave harmonics

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

------------------------------------------------------------------
To unsubscribe from si-list:
si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field

or to administer your membership from a web page, go to:
http://www.freelists.org/webpage/si-list

For help:
si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field

List archives are viewable at:     
                http://www.freelists.org/archives/si-list
or at our remote archives:
                http://groups.yahoo.com/group/si-list/messages 
Old (prior to June 6, 2001) list archives are viewable at:
                http://www.qsl.net/wb6tpu
  
------------------------------------------------------------------
To unsubscribe from si-list:
si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field

or to administer your membership from a web page, go to:
http://www.freelists.org/webpage/si-list

For help:
si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field

List archives are viewable at:     
                http://www.freelists.org/archives/si-list
or at our remote archives:
                http://groups.yahoo.com/group/si-list/messages 
Old (prior to June 6, 2001) list archives are viewable at:
                http://www.qsl.net/wb6tpu

Other related posts: