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Square Waves

Type : waveform generation
References : Posted by Sean Costello

Notes :
One way to do a square wave:

You need two buzz generators (see Dodge & Jerse, or the Csound source code, for implementation details). One of the buzz generators runs at the desired square wave frequency, while the second buzz generator is exactly one octave above this pitch. Subtract the higher octave buzz generator's output from the lower buzz generator's output - the result should be a signal with all odd harmonics, all at equal amplitude. Filter the resultant signal (maybe integrate it). Voila, a bandlimited square wave! Well, I think it should work...

The one question I have with the above technique is whether it produces a waveform that truly resembles a square wave in the time domain. Even if the number of harmonics, and the relative ratio of the harmonics, is identical to an "ideal" bandwidth-limited square wave, it may have an entirely different waveshape. No big deal, unless the signal is processed by a nonlinearity, in which case the results of the nonlinear processing will be far different than the processing of a waveform that has a similar shape to a square wave.





Comments


Added on : 31/03/03 by dfl AT stanford[ DOT ] edu
Comment :
Actually, I don't think this would work...
The proper way to do it is subtract a phase shifted buzz (aka BLIT) at the same frequency. This is equivalent to comb filtering, which will notch out the even harmonics.




Added on : 08/11/08 by sean[ AT ]valhalladsp[ DOT ]com
Comment :
The above comment is correct, and my concept is inaccurate. My technique may have produced a signal with the proper harmonic structure, but it has been nearly 10 years since I wrote the post, so I can't remember what I was working with.

DFL's technique can be implemented with two buzz generators, or with a single buzz generator in conjunction with a fractional delay, where the delay controls the amount of phase shift.            




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