2da Evaluación II Término 2017-2018. Febrero 7, 2018
Tema 4.
S_x(f)= \frac{N_0}{2}
Autocorrelación de Y(t) S_{Y}(f) = |H(f)|^2 S_x(f) = \Big|\frac{1}{1+j2\pi f}\Big| ^2 \frac{N_0}{2} = \Big|\frac{1}{1+(2\pi f)^2}\Big| \frac{N_0}{2} S_{Y}(f) = \frac{N_0}{4} \Big|\frac{2}{1+(2\pi f)^2}\Big| R_{Y}(\tau) = F^{-1} [S_{Y}(f)] = F^{-1} \Big[\frac{N_0}{4} \frac{2}{1+(2\pi f)^2}\ \Big] = \frac{N_0}{4} F^{-1} \Big[\frac{2}{1+(2\pi f)^2}\ \Big] R_{Y}(\tau) = \frac{N_0}{4} e^{-|\tau|}
Potencia promedio
R_{Y}(0) = \frac{N_0}{4} e^{-|0|} = \frac{N_0}{4}