[music-dsp] What is the waveform with even harmonics called

robert bristow-johnson rbj at audioimagination.com
Sat Oct 3 14:23:24 EDT 2009

On Oct 3, 2009, at 2:10 PM, spambait1000006 at cox.net wrote:

> I put a bit up about different waveforms at
> http://members.cox.net/~inicoderocker/waveforms.pdf
> Hopefully there is something of interest and not too much to lead one
> astray.

it's a useful compendium.

a few kind suggestions:

1. the series for square wave on page 1 is wrong.  it does leave out  
the even harmonics, but the strength on the harmonics left are still  
1/m where m is the harmonic number, which you have as 2n-1.  so it  
should be 1/(2n-1) for the coef.  there might be other little errors,  
but that one caught me right off the bat.

2.  i would suggest normalizing the peak max value of the standard  
waveforms.  that will put a constant (maybe with 1/pi in it) in front  
of the whole series.  another possibility would be to normalize the  
first harmonic which you do in most cases.

3.  then when displaying two waveforms, one with the phases in the  
"classic" positions and the other with changed or scrambled phases,  
to have the plot zoom to be the same for the comparable images.  e.g.  
Figs 20 and 21.

4.  if it were me, i would position the squarewave, pwm, and pulse  
trains, to be even symmetry and put the saw in as odd symmetry.  it's  
neat to see the necessary change in sign as the harmonics start  
adding up.


r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."

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