I dont really get the section ** 3.4.2.9 Octave doubler** in the pd-tutorial.com ..

If you delay a periodic signal by the half the duration of one period and add it to the original, the fundamental tone (and all odd partials) is cancelled out

• if my signal is a sinusoid the result is a 0 signal ;
• if my signal come from a phasor (like in the example) the result is a sawtooh at the double freq ranging in [0.5 , 1.5] ;
• if my signal come from a natural instrument (e.g. a cello) how do we explain that it will remove the odd partials ?

thx.

@mx Hello....... as it says in the introduction to that patch...... "If you know the frequency of a signal's fundamental, you can construct an octave doubler as follows: Let's take a wave..."
G06 in pd's docs folder tries to solve the problem using [fiddle]... but G09...... "rotating tape heads" method will probably give better results......
If you want the best solution it could be that provided by Katja Vetter here.......... http://katjaas.nl/pitchshift/soundtouch~.html ....... downloadable at the bottom of the page..
For some reason (that is obvious) I always look first at her site when I need an audio solution, or I just want to understand why I don't understand!
David.

because each odd partial cancels itself out with phase cancellation. Halfway through the wave, every odd partial (sine wave) will also be halfway through a cycle. Therefore, since the sine wave would be negative in the second half of its wave, adding it to the positive part from the beginning of the wave cancels it out. This works for different starting phases also, because whatever phase the partial started at, halfway through the wave will still be the opposite polarity
It's helpful to picture it: picture 3 cycles of a sine wave. Cut them in half, and you will see that there are 1 1/2 cycles in each half, and the second half of the overall wave starts on a negative half of a sine wave