Which is the total energy of the product of two discrete energy signals Assume that I have two signals with finite energy. 

The first, $x_s$
\begin{equation}
E_s = \sum_{i=0}^{N} |x_s(i)|^2
\end{equation}

and the second, $w$
\begin{equation}
E_w = \sum_{i=0}^{N} |w(i)|^2.
\end{equation}

Then, which is the enrgy of the follwoing signal that combine the two ones as follows

\begin{equation}
E_s'=\sum_{i=0}^N |x_s(i) \cdot (1+K w(i))|^2
\end{equation}

In particular assuming $x_s$ and $w$ uncorrelated, is there a way to express $E_s'$ as fucntion of $E_s$ and $E_w$?

Thanks in adavance.

PS: I have already posted a smiliar question here
https://math.stackexchange.com/questions/1560821/which-is-the-total-energy-of-the-product-of-two-discrete-energy-signals
You don't give enough information for an expression of the combined energy in your expression.
$$\begin{eqnarray}
&amp; &amp;\sum_{i=0}^N \left| x_s(i)\cdot\left( 1+K\,w(i) \right) \right|^2 \\
&amp;=&amp;\sum_{i=0}^N \left( x_s(i)\cdot\left( 1+K\,w(i) \right) \right)^\star \times\left( x_s(i) \cdot\left( 1+K\,w(i) \right) \right)\\
&amp;=&amp;\sum_{i=0}^N \left( x_s(i)^\star\,x_s(i) + x_s(i)^\star\,K^\star\,w(i)^\star x_s(i)\,K\,w(i) + x_s(i)^\star x_s(i)\,K\,w(i)+x_s(i)\,x_s(i)^\star\,K^\star w(i)^\star\right)\\
&amp;=&amp;\sum_{i=0}^N \left( |x_s(i)|^2 \times \left(1+2\,\Re(K\,w(i))+|K|^2\,|w(i)|^2 \right) \right)\\
&amp;=&amp;E_s+\sum_{i=0}^N|x_s(i)|^2\left(2\,\Re(K\,w(i))+|K|^2\,|w(i)|^2 \right)
\end{eqnarray}$$

This means you need to know the correlation of the square magnitude of $x_s$ with the real part of $w$ and the square magnitude of $w$. The correlation of just $x_s$ and $w$ does not play any role.