Harmonic composition of a square wave-related question

On 23 Jun 2005 18:30:07 -0700, "davidd31415" <davidd31415@xxxxxxxxx>
wrote:

>I know you can make a square wave from the sum of sinusoidals, but does
>this mean that if you look at a sine-wave that wasn't made by using
>sinusoids (perhaps using a switch or an oscillating crystal to turn the
>signal on and off) on a spectrum analyzer that you would see all of the
>harmonics required to make up the square wave?
___
This post got me to thinking about a related subject. I'm a hobbyist,
and my math is limited to one year of calculus, but I would like to
see if I have a correct conception of what's going on here. I can see
that any periodic function can be put through the Fourier transform to
obtain an infinite series of sin and/or cos terms to completely
describe the original function. This applies to electronic circuits,
musical instruments, vibrational analysis of bridge decks, etc.
So, when one sees a "perfect square wave" on the oscope, it is
actually always a mixture of sine waves of f(fundamental-the frequency
of the square wave as seen on the oscope),3f,5f,7f...... frequencies.
A more complex wave like that produced by a violin string would look
different than either a sine wave or a square wave, because the
mixture of waves producing it are not at the amplitude/frequency
required by the Fourier transform to produce a square wave. If I were
to see what looks like a very low distortion sine wave on the oscope,
I can infer that this is a "true sine" wave, with very little
contribution from any higher harmonics, and not some weird lucky mix
of higher sin/cos frequencies that are significant compared to the
fundamental? Or would the use of a spectrum analyzer be required to be
sure?
For circuit elements like capacitors and inductors, whose reactance
varies with frequency, what happens when dealing with a square wave?
what frequency does one use in the reactance formulas, knowing that
you're dealing with a mixture of them? I would instinctively just put
in the fundamental frequency, but is this right? TIA for clearing any
of this up for me.


.

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