I have a $2\pi$ periodic function which in the interval $[0,\pi]$ is $f(t) = \sin{\frac{t}{2}}$.
I have to find the sum for $t \in \mathbb{R}$. But do I know anything about $f(t)$ outside of $t \in [0,\pi]$?
I also have to find the effect of $f(t)$. Normally, I get the effect as $P(f) = \frac{1}{2\pi} \int_{-\pi}^\pi |f(t)|^2 \, \mathrm{d}t$, but how can I use this if I only know about the function in the interval $[0,\pi]$?
Maybe there is something I have misunderstood about periodic functions?