$$ x(t) = |a \cos(\omega_0 t) + b \cos(\omega_1 t)| $$ with $a, b \geq 0$, $\omega_0, \omega_1 > 0$, but $a, b > 0$ or all $a, b$ (negatives included) is also acceptable, or replacing $\cos$ with $\sin$.
Is there a known result for $\mathcal{F}\{x(t)\}$? Derivation not needed but is welcome. Of main interest is the DFT, but I don't reckon we can find it without $\mathcal{F}$.
Periodicity is maintained for all $a, b$, though I'm unsure how predictable it is depending on $a,b$, from which we could build a periodic windowing function to isolate $d(t)=|y(t)| - y(t)$, where $x(t) = |y(t)|$.
W|A gives for $a \cos(A) + b \cos(B)$
$$ \sum_{k=0}^{\infty} \frac{\cos(k\frac{\pi}{2} + z_0)(a(A - z_0)^k + b(B - z_0)^k)}{k!} $$
for any $z_0$, which for $z_0=0$ is sort of within $2k$ of product of cosines, and we have for the $\sin$ version, from here
$$ c \sin {\left( A + \sin^{-1}\left(\frac{b}{c} \sin (B - A)\right) \right)} $$
where $c = \sqrt{a^2 + b^2 + 2ab \cos(B - A)}$. So even $y(t)$ has nonlinearities...
