How would I calculate the expected correlation of two sawtooth waveforms? That is, the correlation of:
$$\operatorname{corr}(\operatorname{saw}(\theta),\operatorname{saw}(\theta+\delta))$$
where delta is a uniform random variable with a range from $[0,2\pi]$. Sawtooth can be defined to be periodic function such that: $$\operatorname{saw}(x) = \frac{x} \pi - 1,\qquad x \in[0,2\pi]$$
Or alternatively:
$$saw(x) = 2(\frac{x+\pi}{2\pi} -\text {floor}(\frac{x+\pi}{2\pi}))-1$$
EDIT: with simulations I got that the correlation is zero, and the correlation between two saw waveforms as function of the phase angle is a parabola with min=-0.5. Analytic solution would still be nice to have.