How to cancel the fundamental frequency of a waveform?

[marioisaac]

Hi, I am trying to cancel the fundamental frequency of a saw wave by adding a phase inverted sine wave, but it is not working. If a saw wave is a sum of sines, why adding a phase inverted sine wave set to the fundamental frequency of the saw wave does not cancel its fundamental frequency?

Is anyone aware of a technique to cancel the fundamental frequency of a waveform, besides filtering?

[foosnark]

It has to match the fundamental completely perfectly in frequency, (inverse) phase and amplitude to work.

And then the result is just a slightly quieter saw wave one octave higher.

[marioisaac]

Thank you foosnark

It has to match the fundamental completely perfectly in frequency, (inverse) phase and amplitude to work.

By inverting phase AND amplitude the waveform is not changed. Inverting only the phase, or inverting only the amplitude of the sine wave, and adding it to the saw wave, to my understanding it should cancel the fundamental frequency, but it does not. Anyone knows why?

And then the result is just a slightly quieter saw wave one octave higher.

Sonically is quite different than a saw an octave higher, and it gives you the possibility to separate the harmonics of the saw wave and process them independently.

[foosnark]

I didn't mean invert BOTH phase and amplitude, I mean the amplitude must match, and the phase must be exactly inverted.

But yeah, I was thinking of a square wave, where removing the fundamental does create a square wave an octave up, because they are geometrically the same.


With a saw, if you highpass filter it (or cancel the fundamental this way), there's both a psychoacoustic effect where the brain fills in the missing fundamental, and also the fact that a single cycle of the resulting waveform still occurs at the original frequency. Fun discussion of that here: https://www.modwiggler.com/forum/viewtopic.php?t=253744

[j wazza]

its easier to invert the polarity (amplitude direction of the waveform up vs down) than the phase (a 180 degree phase shift - shifting in time), and polarity is more likely to work with things other than sines, but these 2 ways have same effect on a sine

but i dont really get why the sine isnt cancelled from a saw, i thought filters work with phase cancellation but not really sure

[marioisaac]

But yeah, I was thinking of a square wave, where removing the fundamental does create a square wave an octave up, because they are geometrically the same.

By removing the fundamental, the geometric shape of the waveform do change, irrespective of it being a saw wave or a square wave, or any other waveform (besides a sine wave, which will not change it's shape, just disappear).

In regards to adding sine waves and saw waves, the following happens:

Adding two identical sine waves with the same frequency, and shifting the phase of one, will not change the shape of the waveform.

And by adding two identical saw waves with the same frequency, and shifting the phase of one 180° apart, will result in a saw wave an octave higher. So in the case of saw waves, phase difference won't work to cancel them; instead polarity inversion will do.

With a saw, if you highpass filter it (or cancel the fundamental this way), there's both a psychoacoustic effect where the brain fills in the missing fundamental, and also the fact that a single cycle of the resulting waveform still occurs at the original frequency. Fun discussion of that here: https://www.modwiggler.com/forum/viewtopic.php?t=253744

Thanks for the link. In my experience, the missing fundamental is not ''filled by the brain'', it is clearly that the fundamental goes silent, nonetheless, the brain still somehow recognizes that the overtone pattern is built in relation to a lower tone (the absent fundamental frequency).
e. g. if the fundamental of a saw wave is 50 Hz, the overtones will be:
100, 150, 200, 250, and so on; if it's 100 Hz, the overtones will be:
200, 300, 400, 500, and so on, and the brain will somehow recognize these different patterns, and the fundamentals they are built upon.

[Tj Shredder]

And thus its not a saw one octave higher, you still get twice as many partials…
If the brain didn’t do that we couldn’t have much fun listening to music from phone speakers…
But if you want to experiment with partials, better get an additive oscillator. Way easier than trying to fit amplitude and phase of the first partial… First of all, if the saw is saw up, then its a sine with the same phase, if its saw down, its a cosine.
The amplitude of the first partial is not 1, its much, much lower!

[9b0]

I just made a video about this. A simple SVF notch tuned to the frequency of the oscillator is sufficient for removing the fundamental. Cancellation using a sine wave works, but it's tedious and not as efficient as the filter tied to the oscillator.

https://youtu.be/u1ut1umKmRg

I hope, it helps!