Course code & title : Session : Time allowed :
EE3210 Signals and Systems Semester B 2019/20
Two hours
CITY UNIVERSITY OF HONG KONG
This paper has twelve pages (including this cover page).
1. This paper consists of 5 questions.
2. Answer ALL questions.
This is an open-book examination.
Students are allowed to use the following materials/aids:
Portable battery operated calculator, Course Handout
Materials/aids other than those stated above are not permitted. Students will be subject to disciplinary action if any unauthorized materials or aids are found on them.
* If you face any technical issue during the exam, please contact the departmental hotline (3442-7740).
Student ID: EE3210 – Final Exam Page 2 of 12
Honor Pledge
Please review the following honor code, then sign your name and write down the date.
1. I pledge that the answers in this exam are my own and that I will not seek or obtain an unfair advantage in producing these answers. Specifically,
(a) I will not plagiarize (copy without citation) from any source;
(b) I will not communicate or attempt to communicate with any other person during the exam;
(c) neither will I give or attempt to give assistance to another student taking the exam; and
(d) I will use only approved devices (e.g., calculators) and/or approved device mod- els.
2. I understand that any act of academic dishonesty can lead to disciplinary action.
Signature
Date
Student ID: EE3210 – Final Exam
Page 3 of 12
Question 1 (20 points)
Find the correct Fourier Transform (or Inverse FT) of the given signals.
(a) (5 points)
(i) 2α
α2 + (2πf)2 (iii) 2α
F e−α|t|, α > 0 (ii) 1
(b) (5 points)
(α + j2πf)2
α2 + (2πf)2 (iv) 2α
F sinc2(t) · cos (4πt) , α > 0
(i) 1 [tri(f−2)−tri(f+2)] (ii) 1[tri(f−2)+tri(f+2)] 2j 2
(α − j2πf)2
(iii) 4π
(1 + j2πf)2 + 16π2
(c) (5 points)
F τ tri τ ∗ τ tri τ , wheretri(t)= 0, otherwise
(i) 1[sinc(f−1)+sinc(f+1)] (ii) 1 [sinc(f−1)−sinc(f+1)] 2 2j
t
t
1 − |t|, |t| < 1
(iv)
1 + j2πf
(1 + j2πf)2 + 16π2
(iii) τ2sinc2 (f · τ)
(d) (5 points)
(iv) τ4sinc4 (f · τ)
F−1 1 4 + j8πf + 4π2 (1 − f2)
(i) (iii)
1 e−2t sin (2πt) u(t) 2π
1 e−2t sin (2πt) 2π
(ii) (iv)
1 e−2t cos (2πt) u(t) 2π
1 e−2t cos (2πt) 2π
Student ID: EE3210 - Final Exam Page 4 of 12
(Answer Page for Question 1)
Student ID: EE3210 - Final Exam Question 2 (20 points)
Consider the following system function H(s) of an LTI system. (a) (6 points) Choose the ROC for a stable system.
Page 5 of 12
(i) {Re(s) < −2} (iii) {−1 < Re(s) < 1}
H(s) = s (s+2)(s+1)(s−1)
(ii) {−2 < Re(s) < −1} (iv) {Re(s) > 1}
(b) (8 points) Choose the ROC for a causal and stable system.
H(s) =
1 (s+4)(s+3)(s+1)2
(ii) {−4 < Re(s) < −3} (iv) {Re(s) > −1}
(i) {Re(s) < −4}
(iii) {−3 < Re(s) < −1}
(c) (6 points) Choose the ROC for a causal system.
H(s) =
s + 1
(s2 +4s+5)(s+3)(s−1)
(ii) {−3 < Re(s) < −2} (iv) {Re(s) > 1}
(i) {Re(s) < −3} (iii) {−2 < Re(s) < 1}
Student ID: EE3210 - Final Exam Page 6 of 12
(Answer Page for Question 2)
Student ID: EE3210 - Final Exam Page 7 of 12
Question 3 (20 points)
Consider a continuous LTI system described by the following input-output relationship.
dy(t) ∞ −t
x(τ)z(t−τ)dτ−x(t), wherez(t)=e u(t)+δ(t).
dt +10y(t)=
(a) (10 points) Find the frequency response H(f) = Y (f) of this system.
X(f)
−∞
(b) (10 points) Determine the impulse response h(t) of the system.
Student ID: EE3210 - Final Exam Page 8 of 12
(Answer Page for Question 3)
Student ID: EE3210 - Final Exam Page 9 of 12
Question 4 (20 points)
Consider LTI systems whose input-output relationship is described by the given equations.
a) (10 points) Find the step response y(t) using the bilateral Laplace Transform. d2y(t) + 6dy(t) + 8y(t) = dx(t)
dt2 dt dt
b) (10 points) Solve the following integral equation using the unilateral Laplace Transform.
tt−τ
y(t)=e 4+4 e y(τ)dτ , t≥0 0
Student ID: EE3210 - Final Exam Page 10 of 12
(Answer Page for Question 4)
Student ID: EE3210 - Final Exam Page 11 of 12
Question 5 (20 points)
Consider a discrete system described by the following difference equation
y[n]=3y[n−1]−1y[n−2]+x[n], |z|>1 482
(a) (8points)DerivethesystemfunctionH(z)andtheimpulseresponseh[n]usingZ-transform.
(b) (6 points) Answer whether this system is causal (or not).
(c) (6 points) Determine the step response y[n] given that |z| > 1.
Student ID: EE3210 – Final Exam Page 12 of 12
(Answer Page for Question 5)