Calculate power of a signal

Question

The task is to calculate power of signal below:

$$ x(t)=\sum^{\infty }_{k=-\infty }(t-k)[u(t-k)-u(t-k-1)]$$

The answer is 0.33 but I don't know how to calculate this even though I applied the formula, then I don't know what should I do next:

$$ \lim_{T\rightarrow \infty}\frac 1 T \int^{T/2}_{-T/2}\left(\sum^{\infty}_{k=-\infty}(t-k)[u(t-k)-u(t-k-1)] \right)^2dt$$

Can someone help me with this, thank you so much

Answer 1

HINT:

The given signal $x(t)$ is periodic. The power of a $T$-periodic signal is given by

$$P_x=\frac{1}{T}\int_0^{T}|x(t)|^2dt\tag{1}$$

That should simplify things for you because you just need to integrate over one period. Just figure out the period $T$ and compute $(1)$. The result is indeed $P_x=\frac13$.