Let $w$ be a complex periodic wave with an infinite number of harmonics. What is the required number of samples $N$, phase-shifted incrementally by equal steps of $2\pi/N$, in order to eliminate harmonics up to the $j$th order through phase-cancelation?
My intuition says I would need $lcm(1, 2, 3, ..., j)*2$ samples so that there is a corresponding antiphase for all frequencies at each phase-shift increment. For instance, if I wanted to eliminate harmonics up to the 2nd order, I would need 4 samples with $\pi/2$ phase-shift increments. For the fundamental frequency, the phase-shifted pairs at increments [$0 - \pi$] and [$\pi/2 - 3\pi/2$] would be in antiphase relationship and cancel each other. Likewise, the second harmonic would be eliminated by the phase-cancelation of pairs at [$0 - \pi/2$] and [$\pi - 3\pi/2$] increments.
I was wondering if there is a better way that can minimize $N$. I'm not from a math-heavy background so I would appreciate laymen explanations.
Thanks!