Let x(t) and y(t) be two orthogonal signals so that integral x(t)y(t) by dt with (-inf

Question

Let x(t) and y(t) be two orthogonal signals so that integral x(t)y(t) by dt with (-inf <t<inf) . Their respective energy values are Ex and Ey. Obtain the energy of the signal x(t)+y(t) and show that it is identical to the energy of the signal x(t)-y(t). Classify if the resulting signal is a power or energy signal.

anonymous · Answer

$$\int\limits\limits_{-\infty}^{\infty}$$

nikvist · Answer

$$E_x=\int\limits_{-\infty}^{-\infty}x^2(t)dt\quad,\quad
E_y=\int\limits_{-\infty}^{-\infty}y^2(t)dt$$
$$E_{x\pm y}=\int\limits_{-\infty}^{-\infty}(x(t)\pm y(t))^2dt=$$
$$=\int\limits_{-\infty}^{-\infty}x^2(t)dt+\int\limits_{-\infty}^{-\infty}y^2(t)dt\pm 2\underbrace{\int\limits_{-\infty}^{-\infty}x(t)y(t)dt}_{=0}=$$
$$=E_x+E_y$$

anonymous · Answer

Thanks pal