Re: Harmonic composition of a square wave-related question
- From: Charles Jean <alchemcj@xxxxxxxxxxxxx>
- Date: Sat, 25 Jun 2005 21:43:50 GMT
On Sat, 25 Jun 2005 01:35:44 GMT, Charles Jean
<alchemcj@xxxxxxxxxxxxx> wrote:
>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.
>
___
Thanks for all the great insights you folks provided! They cleared up
some of the fog. I thought John's idea of putting the signal through a
good low-pass filter was a quick, semi-quantitative test for the
presence of significant harmonics was especially neat. Any good
references on how to design/build a decent one? Is it possible to
make one that has a variable cut-off frequency? Or is there a circuit
out there somewhere for a "poor-boy" RF spectrum analyzer?(0.5-30
MHz). Please remember that any thing above elementary calculus leaves
me with puzzled look on my face-this includes differential equations!
Thanks again for the great responses.
Charlie
.
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