Hi!

Kind of ashamed of myself to ask help for this dumb stuff, but I really can't see what could be the problem.

I am trying to illustrate Fourier's theorem by summing a few osc to make a sawtooth. However, the sawtooth won't appear, though I think I used the right formula.

http://www.pdpatchrepo.info/hurleur/fourier2.pd

Do you mean you can't see anything or that it doesn't look like a sawtooth?

I could see a waveform OK when I ran your patch (with DSP on, of course), but you need to make two changes to make it look like a sawtooth:

1. The signs of the harmonic components must alternate. Try making the scaling factors for all your even harmonics negative.

2. The harmonics must be in sine phase, but osc~ starts off in cosine phase. Simultaneously send 0.25 to all the phase inlets of your oscs to get them in sine phase relative to each other.

Aaww! Yes! My problem was that even though in theory I should know how to re-synthesize a sawtooth I couldn't get the right shape...

In fact, if I remembered a bit more my maths, I could have guessed what the phase was from the formula

Thanks a lot!!!

just a suggestion: if you want to create a sawtooth wave of multiple sine partials, it might be a better idea to use an array, fed with a "sinesum" message and a tabosc4~ or tabread~. at least in respect of cpu usage, this might be more efficent.
check out this here: http://en.flossmanuals.net/pure-data/ch024_generating-waveforms/

Thanks! I know ... I just wanted to illustrate how to approximate a sawtooth using additive synthesis. So I have 10 partials, and you can toggle them on and off, and see the result change and getting little by little closer to a sawtooth