[SI-LIST] Re: Square wave harmonics

Hi Lucien,

Your questions are somewhat philosophical and I'll try to answer.

Generally speaking, there is the physical world where natural laws 
determine how things work.  We try to understand these laws, but our 
understanding is never complete.

We devise models, concepts and ideas of how the real world works.  These 
models are not the same thing as the real world though.  Mathematics allows 
descriptions of models.  Models always have simplifying assumptions.

A Fourier series model of a square wave assumes the signal was turned on at 
the beginning of time and won't be shut off until the end of time 
(infinity).  Physically that's nonsense, but it allows the math to work and 
be simpler.  So in many cases this model is a very good approximation of 
physical reality.  Moreover it is very useful for us to understand and 
communicate characteristics of a signal.  A better model would be a Laplace 
transform since the signal is turned on and off, but the Fourier model may 
be close enough.  Remember the choice of the model depends on the 
problem.  There are other models for signals (like a signal is represented 
by a vector) that you'll learn about later.

Make a distinction between the model and physical reality.  For example, we 
have different ideas about what an atom is, particle, or wave, or 
wave-particle.  But we really don't know exactly what an atom is.

Many spectrum analyzers are actually a radio receiver that automatically 
sweeps over the frequency range.  Some spectrum analyzers sample the time 
data and use a computer to calculate the Fourier transform to deduce the 
frequency spectra.


Chuck


At 02:59 PM 11/26/01, 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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