P$1.$ Consider the signal

a$)$ Find the PSD $$and the autocorrelation $$

b$)$ If is an input to the LP filter whose frequency response is$,$ find the PSD of the corresponding output.

c$)$ What is the equivalent noise bandwidth of$?$

$$

$$

P$2.$ Given a linear filter with frequency response given by

$$

$$ The input is $$where $$is a r$.$v$.$ uniformly distributed between $0$ and $$and n$($t$)$ is a white noise with PSD

$$ Find the signal$-$ to$-$ noise power ratio $($SNR$)$ at the filter output.