Suppose that a white Gaussian noise
X
t
X
t
is input to a linear system with transfer function given by

Hf={1 if |f|≤20 if |f|>2
H
f
1
f
2
0
f
2

(1)
Suppose further that the input process is zero mean and has spectral
height

N
0
2=5
N
0
2
5
.
Let

Y
t
Y
t
denote the resulting output process.

a) Find the power spectral density of
Y
t
Y
t
.
Find the autocorrelation of
Y
t
Y
t
(i.e.,
R
Y
τ
R
Y
τ
).

b) Form a discrete-time process (that is a sequence of
random variables) by sampling
Y
t
Y
t
at time instants T seconds apart. Find a value for T such that
these samples are uncorrelated. Are these samples also
independent?

c) What is the variance of each sample of the output process?