A white Gaussian noise process of zero mean and power spectral density N0/2 is applied to the filtering scheme shown in Figure. The noise at the low-pass filter output is denoted by n(t).

a. Find the power spectral density and the autocorrelation function of n(t).

b. Find the mean and variance of n(t).

c. What is the maximum rate at which n(t) can be sampled so that the resulting samples are essentially uncorrelated?