Harmonics question

[Magnus Danielson]

>>>>> "S" == Stopp,Gene  <gene.stopp at telematics.com> writes:

 >> 
 >> I understand that a square wave is made up of sine waves, but what are
 S> the
 >> exact frequencies that the harmonics oscillate at?  For example, if you
 >> have a square wave at 130Hz are all the harmonics octaves up and down
 S> from it?
 >> 

 S> Hey, I can answer that....

[Stuff deleted]

 S> This is just a quickie explanation off the top of my head. There are
 S> much more in-depth explanations, and one I can think of is an article in
 S> an old Electronotes that has all the math.

Gene missed one term, the DC term which may also exist. It does have
practical importance to analog synths since the existence of a DC term
is causing a thumping noise.

Being a bit overprecise I would say that you can view a periodic
waveform as being built up by a number of sines and a DC term. When
Joseph Fourier (who discoverd this while investigating
heat-distributions in rods of metal) proposed this to the French
Scientific Academy (I recall 1810 or something in the back of my head)
he where basically laugthed out of there. It where just too obscure at
the time. Today we use the Fourier Transform in many ways and harmonic
analysis is just a diffrent name.

In saying periodic waveforms this not only eliminates waveforms with
no selfsimilarity but also waveforms that changes amplitude over time,
for that you need to add some more stuff. But this is a diffrent
league of problems.

Anyway, for that 130 Hz squarewave you would get

DC, 130Hz, 390Hz, 650 Hz etc.

For a perfect squarewave will DC however be 0.

Confusingly Yours,
Magnus