Question

Let X(t) be a white Gaussian noise with power spectral density $\frac{3}{2}$ W/Hz. If X(t) is input to an LTI system with impulse response $e^{-t}u(t)$. The average power of the system output is ___________ W (rounded off to two decimal places).

Hint:

The average power of a signal can also be found by integrating the squared magnitude of its impulse response if the input is white noise with unity PSD. For a general white noise input with PSD $N_0/2$, the output power is $P_Y = (N_0/2) \int_{-\infty}^{\infty} |h(t)|^2 dt$. This avoids Fourier transforms. Here, $\int_0^\infty (e^{-t})^2 dt = 1/2$, so $P_Y = (3/2) \times (1/2) = 3/4 = 0.75$.

Answer 1

Correct Answer: 0.24