University of Technology
Department of Electromechanical Engineering
First Term Exam /2020-2021
Branch: Electromechanical Systems
Subject: Signals and Systems
Fourth Year
Examiner: Dr. Manal Kadhim
Exam Time: 1:5 hours
Date: 20/3/2021
π
π
3
2
Q1:(a) Let x(t) = sin ( t) + cos ( t) . Determine if
this signal
is periodic or non
periodic , If periodic determine the fundamental period.
(3 Marks)
(b) Carefully sketch the following signal:
𝑥(𝑡) = −𝑢(𝑡 + 3) + 2𝑢(𝑡 + 1) − 2𝑢(𝑡 − 1) + 𝑢(𝑡 − 3)
(2 Marks)
t
Q2: For the system y(t) = x ( ). Determine whether it is linear, time invariant, memory,
3
and causal. Justify you answers.
(5 marks)
1 𝑛
Q3:(a) Calculate the average power and energy of the DT signal 𝑥 [𝑛] = ( ) u[n] , and
2
classify this signal as power or energy signal.
(2 Marks)
(b) Consider the original signal spectrum given in Figure (1), Draw the sampled spectrum
|X s (f)|for the following cases. fs = 400Hz , fs = 200Hz and fs = 100Hz
X (f)
f(Hz)
- 100
100
Figure (1)
(3 Marks)
Good Luck
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