Re: square wave harmonic theory (time domain)

On May 31, 3:00 pm, "Thomas Magma" <somewh...@xxxxxxxxxxxxxxxxxx>
wrote:
Here's another graphic:
http://slack.net/~ant/bl-synth/4.harmonics.html

Cheers!
Rich

I have generated a square wave many times on my graphics calculator and
using Goldwave's expression evaluator with expressions like:

sin(2*pi*f*t) + sin(2*pi*f*t*3)/3 + sin(2*pi*f*t*5)/5 + sin(2*pi*f*t*7)/7 +
sin(2*pi*f*t*9)/9 + sin(2*pi*f*t*11)/11 + sin(2*pi*f*t*13)/13 +
sin(2*pi*f*t*15)/15 + sin(2*pi*f*t*17)/17 + sin(2*pi*f*t*19)/19 +
sin(2*pi*f*t*21)/21 + sin(2*pi*f*t*23)/23 + sin(2*pi*f*t*25)/25 +
sin(2*pi*f*t*27)/27 + sin(2*pi*f*t*29)/29 + sin(2*pi*f*t*31)/31 +
sin(2*pi*f*t*33)/33 + sin(2*pi*f*t*35)/35 + sin(2*pi*f*t*37)/37 +
sin(2*pi*f*t*39)/39 + sin(2*pi*f*t*41)/41 + sin(2*pi*f*t*43)/43 +
sin(2*pi*f*t*45)/45 + sin(2*pi*f*t*47)/47 + sin(2*pi*f*t*49)/49 +
sin(2*pi*f*t*51)/51 + sin(2*pi*f*t*53)/53 + sin(2*pi*f*t*55)/55 +
sin(2*pi*f*t*57)/57 + sin(2*pi*f*t*59)/59 + sin(2*pi*f*t*61)/61 +
sin(2*pi*f*t*63)/63 + sin(2*pi*f*t*65)/65 + sin(2*pi*f*t*67)/67 +
sin(2*pi*f*t*69)/69 + sin(2*pi*f*t*71)/71 + sin(2*pi*f*t*73)/73 +
sin(2*pi*f*t*75)/75 + sin(2*pi*f*t*77)/77 + sin(2*pi*f*t*79)/79 +
sin(2*pi*f*t*81)/81 + sin(2*pi*f*t*83)/83 + sin(2*pi*f*t*85)/85 +
sin(2*pi*f*t*87)/87 + sin(2*pi*f*t*89)/89 + sin(2*pi*f*t*91)/91 +
sin(2*pi*f*t*93)/93 + sin(2*pi*f*t*95)/95 + sin(2*pi*f*t*97)/97 +
sin(2*pi*f*t*99)/99

You can still see the harmonics in the time domain.

But I've also made perfect square waves with logic expressions like:

int(2*f*t)%2*2-1

Similar to how one would generate them is say a micro or clock counter.
Where there is no harmonic content whatsoever in the time domain.

Thomas

I was going to post something longer when I realized we're going
around in circles. Then again maybe you're NOT going around in circles
when you should be ;-)

Go read up on Fourier Series, then Fourier Transform and then
Discrete Fourier Transform.

--
Joe

.

Relevant Pages

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