1
Full Name: ANSWERS
Do not put any explanations or work in this answer sheet. Only your answers will be considered.
Problem 1
(8%)
Is the system:
2% (a) Linear?
YES
NO
CAN’T TELL
2% (b) Time-invariant?
YES
NO
CAN’T TELL
2% (c) Causal?
YES
NO
CAN’T TELL
2% (d) Stable?
YES
Problem 2
NO
CAN’T TELL
(4%)
Is the system:
2% (a) Causal?
YES
NO
CAN’T TELL
2% (b) Stable?
YES
NO
CAN’T TELL
Problem 3
(4%)
Is the system:
2% (a) Causal?
YES
NO
CAN’T TELL
2% (b) Stable?
YES
NO
CAN’T TELL
Problem 4
(6%)
Hxy (z) =
1+3z −1
1− 12 z −1
Hey (z) =
1
1− 12 z −1
Problem 5
H(ejω ) =
Problem 6
(5%)
1+ 12 e−jω
1− 13 e−jω
(9%)
3% (a) my [n] = 0
3% (b) φyy [m] =
1
3
3% (c) Pyy (ejω ) =
Please turn over
(2δ[m] + δ[m − 1] + δ[m + 1])
2
3
(1 + cos ω)
2
Problem 7
3% (a) H2 (z) =
(7%)
1− 14 z −1
1− 12 z −1
3% (b) H2 (z) unique within a scalar factor?
YES
NO
3% (c) Are x[n] and y[n] uncorrelated?
YES
NO
Problem 8
(8%)
The maximum such interval T is:
Problem 9
π
Ω1 +Ω2
(9%)
5% (a) The largest possible T is: strictly less than 10−4
4% (b) The estimate of A is
Problem 10
EXACT
APPROXIMATE
(8%)
4% (a) yc (t) is xc (t) delayed by 3.7T1 and then stretched in time by
T2
T1 .
4% (b) yd [n] is the sequence obtained by delaying xc (t) by 3.7T1 and then sampling at period T1 .
Problem 11
(4%)
Is the overall system LTI?
Problem 12
NO
YES
(4%)
y[n] = δ[n + 1] + 4δ[n] + 8δ[n − 1] + 8δ[n − 2] + 3δ[n − 3]
Problem 13
4% (a)
4% (b)
(8%)
(i) Stable?
YES
NO
CAN’T TELL
(ii) Causal?
YES
NO
CAN’T TELL
YES
(i) Stable?
(ii) Causal?
Problem 14
YES
NO
NO
CAN’T TELL
CAN’T TELL
(6%)
y(t) = s(t) cos (Ωc t + φ0 )
Problem 15
(8%)
y[n] = (Circle one)
Problem 16
y1 [n]
y2 [n]
(0%)
The best estimate of my grade is: 100
y3 [n]
y4 [n]
y5 [n]
y6 [n]
y7 [n]
y8 [n]