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

Jeremy Shaw jeremy at n-heptane.com
Mon Jun 15 16:03:25 EDT 2009


Hello,

What is the name of the waveform which has even harmonics which fall
off at 6dB/octave?

By comparison:

 sawtooth wave = even + odd harmonics falling off at 6dB/octave
 square        = odd harmonics falling off at 6dB/octave
 triangle wave = odd harmonics falling off at 12dB/octave

You can see what it looks like using this matlab/octave code:

# even wave
N = 2000;
t = ([0:1000] / 1000) * 4 * pi;
f = zeros (1,1001);
for k = [1,(1:2:N)+1]
  f = f + sin (k * t) / k;
end
f = f * 0.88678;
plot(t,f)
set(gca,'XTick',0:pi/2:4*pi)
set(gca,'XTickLabel',{'0','pi/2','pi','3pi/2','2pi','5pi/2','3pi','7pi/2','4pi'})
grid on
axis normal

Are there any nifty ways to generate this waveform efficiently?

thanks!
- jeremy


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