What is the average of $\DeclareMathOperator{\rect}{rect} \rect(\cos(\pi t/2)) $? We have this signal:
$$\operatorname{rect}\left(\cos\left(\frac{\pi t} {2}\right)\right) $$
I must find the average power , how can i get there ?
My solution:
I have seen that
$$-\frac 12 &lt; \operatorname{rect}\left(\cos\left(\frac{\pi t}{2}\right)\right) &lt; 1$$
is for
$$\frac 23+k \pi &lt;t &lt; \frac 43 + k\pi$$
so in a period it should be rectangular pulse , but how do I calculate the average ?
The given signal is clearly periodic. So just follow these steps and find the solution:

Find the period $T$.
Figure out the interval within a period for which the signal equals $1$.
Compute the average: $$\overline{x(t)}=\frac{1}{T}\int_0^Tx(t)dt$$

If you're convinced that you did everything right, don't worry about a given solution which is different.