Extract parameters of a single harmonic
I tried something that I didn't thought of before: 

force $\omega_0$ to be a multiple of $2 \pi \frac{fs}{N}$, with $fs$ my sampling rate.

And of course, this is what happens in the fft.



I only ask myself if I can get the same results for $\omega_0\neq2 \pi \frac{k}{N} fs$