Re: square wave harmonic theory (time domain)
- From: The Phantom <phantom@xxxxxxx>
- Date: Thu, 31 May 2007 14:14:54 -0700
On Thu, 31 May 2007 19:00:54 GMT, "Thomas Magma"
<somewhere@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.
Try this for a surprise:
F(t) = 1.22860622406 * sin(2*pi*t)
+ .307151556015 * sin(2*pi*t*3)
+ .102383852005 * sin(2*pi*t*5)
+ .0292525291443 * sin(2*pi*t*7)
+ .0062050819397 * sin(2*pi*t*9)
+ .000846147537231 * sin(2*pi*t*11)
+ .0000550746917725 * sin(2*pi*t*13)
What do you see in the time domain? You will have to plot it on a PC
rather than a calculator to see how good it really is.
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
.
- References:
- square wave harmonic theory (time domain)
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