[SI-LIST] Re: Square wave harmonics

I don't think the distinction you make between "modeled" or "represented
by" and "physically composed of" is as big a one as you're making it out
to be.

Of course the HP function generator does not create a square wave by
adding a bunch of sine waves. But the harmonics are, nonetheless,
physically present in the waveform, so your engineering colleagues are
in fact correct.

If you had a perfect filter that filtered the fundamental frequency, and 
you
input your square wave, the output would be a sine wave at the 
fundamental
frequency.  And so on for filters of all the odd harmonics (the even 
harmonics
not being present in a square wave, if memory serves me). And the 
amplitudes
of each of these would be exactly what a Fourier series would predict.

Just about all radio technology is based on this. In the old (tube) days,
to get a VHF frequency, you'd bias an amplifier in (I think) class C 
operating
region to generate a bunch of harmonics, then tune out the one you're
interested in--this is how frequency doublers and triplers worked. If you
looked at the unfiltered output of such an amplifier, it would not be 
apparent
that it bore much relation to the input or anything else, but the 
harmonics
are, so to speak, there just waiting to be selected out by a tuned 
circuit.


On Monday, November 26, 2001, at 01:59 PM, 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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Kim Helliwell
Apple Computer
kimgh@xxxxxxxxx
408 974 9936

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