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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.

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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) $.

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