# Finding the Energy & Power of a Composition of Odd and Even Signal

Given two CT signals $$x_1(t)$$ (even signal) and $$x_2(t)$$ (odd signal). If $$x_1(t)+x_2(t)$$ is an even signal then what is the energy and power of $$x_2(t)$$.

My Attempt

$$\int \limits _{-\infty}^{+\infty}$$ $$\left| x_1(t)+x_2(t)\right|^2 dt$$

Since the functions are real we can

= $$\int \limits _{-\infty}^{+\infty}$$ $$\left( x_1(t)+x_2(t)\right)^2 dt$$

= $$\int \limits _{-\infty}^{+\infty}$$ $$x_1^2(t)dt$$ + $$\int \limits _{-\infty}^{+\infty}$$ $$x_2^2(t)dt$$ + $$\int \limits _{-\infty}^{+\infty}$$ $$2 x_1(t) x_2(t)dt$$

This one was useful for the next step

= $$\int \limits _{-\infty}^{+\infty}$$ $$x_1^2(t)dt$$ + $$\int \limits _{-\infty}^{+\infty}$$ $$x_2^2(t)dt$$

Now the energy of $$x_2(t)$$ is the difference between the energy of $$x_1(t) +x_2(t)$$ and that of $$x_1(t)$$.

We know that $$x_1(t)$$ is even , $$x_1(t)+x_2(t)$$ is even , $$x_2(t)$$ is odd (however its energy function $$x_2(t)^2$$ is even since its product of two odds)

~~ And I'm stuck here ~~~

• I think I figured this out (: I'll try to write the answer asap – AcademicalResearcher Aug 16 '20 at 15:22