How to calculate the discrete power of a discrete signal? 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.
The instantaneous power is simply $p(k) = x^2(k)$. The signal energy is given by $W_x = \sum_{k=0}^{k=N} x^2(k) $.