COMSATS University Islamabad, Abbottabad Campus

Department of Electrical and Computer Engineering

Mid Term Fall 2022

Class: BCE/EPE/EEE-4R Date: Nov. 17, 2022

Subject: Signals & Systems Instructor: Dr. Alam Zaib
Time Allowed: 1 ½ hrs Max Marks: 50
Name:___________________________ Registration #______________

Course Learning Program Learning

Domain /
Question Objective Objective
Level Justification
(CLO) (PLO)

1 CLO-0 PLO-0 - MCQs

Describe and distinguish
Cognitive/
2 CLO-1 PLO-1 between CT and DT signals
C2
and systems
Cognitive/ Apply convolution to
4 CLO-2 PLO-1
C3 characterize LTI systems
Frequency analysis of
Cognitive/
3,5 CLO-3 PLO-2 periodic signals using
C4
Fourier Series

Instructions:
 Mobile phones, electronic gadgets and any other communication devices are not allowed.
 MCQs should be solved on the given sheet
 Write your class section visibly on the answer sheet
 Give details of your work to earn maximum score … Good Luck!

1
 SECTION-A (Objective Type)
(Time allowed: 10 min) (Marks: 10)

Name: _______________________ Registration #_____________________ Class:________

Q.1) Choose the best option against ANY TEN of the following MCQs.

1. The signal 𝑥(𝑡 + 2) can be obtained from 𝑥(𝑡) by:

(a) Shifting to the right
(b) Shifting to the left
(c) Shifting upward
(d) Shifting downward

2. The signal 𝑥[3𝑛 + 1] can be obtained from 𝑥[𝑛] by:

(e) expanding
(f) compressing
(g) shifting and expanding
(h) shifting and compressing

3. A power signal is characterized by:

(a) Finite energy
(b) Infinite energy
(c) Zero energy
(d) Infinite power

4. The power of a sinusoidal signal 𝑥(𝑡) = 10 cos(𝜋𝑡) , ∀𝑡 is:

(a) 5 watt (b) 10 watt (c) 50 watt (d) 100 watt

5. The signal 𝑢(1 + 𝑡) is zero over the interval:

(a) 1 < 𝑡 < ∞ (b) −1 < 𝑡 < ∞ (c) −∞ < 𝑡 < 1 (d) −∞ < 𝑡 < −1

6. The complex number 𝑧 = (1 − 𝑗)/√2 has magnitude of:

(a) −2 (b) 2 (c) −1 (d) 1

7. An LTI system can be mathematically described/modelled by:

(a) differential/difference equation
(b) impulse response
(c) input/output equation
(d) all of them

2
8. A system described by I/O relation: 𝑦(𝑡) = 2𝑥(𝑡 − 1) is:
(a) memoryless
(b) non-causal
(c) stable
(d) all of them

9. A continuous-time periodic signal 𝑥(𝑡) has Fourier series coefficients: 𝑎−2 = −𝑗, 𝑎2 = 𝑗. The
power of 𝑥(𝑡) is:
(a) 1 watt
(b) 2 watt
(c) 3 watt
(d) 4 watt

10. The frequency of the 2nd harmonic component of Fourier series of periodic signal 𝑥[𝑛] with
period 𝑁 = 4 is:
(a) 𝜋/2 rad/samp
(b) 𝜋 rad/samp
(c) 2𝜋 rad/samp
(d) 2𝜋/3 rad/samp

11. For any signal 𝑥(𝑡), the product: 𝑥(𝑡)𝛿(𝑡 − 2) = _____________?

(a) 𝑥(0)𝛿(𝑡) (b) 𝑥(2) (c) 𝑥(2)𝛿(𝑡) (d) 𝑥(2)𝛿(𝑡 − 2)

12. For any signal 𝑥(𝑡), the convolution: 𝑥(𝑡) ∗ 𝛿(𝑡 − 2) = _____________?
(a) 𝑥(2)𝛿(𝑡 − 2) (b) 𝑥(𝑡) (c) 𝑥(𝑡)𝛿(𝑡 − 2) (d) 𝑥(𝑡 − 2)

3
 SECTION-B (Subjective part)
(Time allowed: 40 min) (Marks 20)

Name: ___________________________ Registration #______________

Q.2) Attempt ANY THREE parts.

(a) Distinguish between energy and power signals. Write mathematical formula for
computing the energy of a continuous-time signal 𝑥(𝑡).

(b) Give clear sketch of: 𝑥(2 − 𝑡), where the signal 𝑥(𝑡) is depicted below.
x(t)
2

t
-1 0 1 2 3

(c) A discrete-time system is described by I/O relation: 𝑦[𝑛] = 𝑥[2𝑛 − 1]. Determine if
the system is linear and time-invariant (LTI)?

(d) Give block diagram of the system represented by the difference equation:
𝑦[𝑛] + 0.5𝑦[𝑛 − 1] = 2𝑥[𝑛 − 1]

Q.3) Apply Fourier series to determine the signal 𝑥(𝑡) whose frequency spectrum is depicted
below. The period of 𝑥(𝑡) is 1 sec.
ak
1

OR k
-2 -1 0 1 2

Find the frequency response i.e., 𝐻(𝑗Ω) of LTI system, described below by the differential
equation. Also compute the magnitude & phase of 𝐻(𝑗Ω) corresponding to Ω = 1.
𝑑𝑦(𝑡) 𝑑𝑥(𝑡)
2𝑦(𝑡) + =
𝑑𝑡 𝑑𝑡

4
 SECTION-C (Subjective part)
(Time allowed: 40 min) (Marks 20)

Q.4) Apply convolution integral to compute the convolution: 𝑦(𝑡) = 𝑥(𝑡) ∗ ℎ(𝑡), where 𝑥(𝑡)
and ℎ(𝑡) are depicted below. Also sketch the signal 𝑦(𝑡).

x(t) h(t)
1 1

t t
0 2 -2 0
OR

Apply convolution sum to compute the convolution: 𝑦[𝑛] = 𝑥[𝑛] ∗ ℎ[𝑛], where 𝑥[𝑛] and
ℎ[𝑛] are depicted below. Also sketch the signal 𝑦[𝑛].

x[n] h[n]
1 1

n n
0 1 2 3 -3 -2 -1 0

Q.5) Determine the Fourier series coefficients 𝑎𝑘 of the periodic continuous-time signal 𝑥(𝑡)
depicted below and plot the frequency spectrum.

x(t)
1
... ...
t
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1