If I have a time series defined by a series like
$$
x = [a_1, a_2, a_3, ..., a_n]
$$
for time from $t = 1$ to $t = n$
How can I get to the power of the signal in this form: $$ P_x = [p_1, p_2, p_3, ..., p_n] $$ Can I use this formula and make it so $N_0 = N_1$
$$ P_x=\frac{1}{N_1-N_0+1}\sum_{n=N_0}^{n=N_1}\left|x(n)\right|^2 $$
Then calculate the $P$ value for every instance in $X(t)$?
Thank you.