ELEC242W
Available time: 75 minutes
CT Signals and Systems
Question 1 (5 marks):
Consider a continuoustime LTI system which has impulse response of h(t ) . The signal
x (t ) is applied at the input of this system. Draw the system output y (t ) versus ti
ELEC242
Sample Final Exam
CT Signals and Systems
Question 1:
Consider a continuoustime system which has input of signal x(t ) and output of y (t ) = x(t )u (t ) .
a) Is this system time invariant? Justify your answer.
b) Is this system linear? Justify yo
ELEC242/U ContinuousTime Signals and Systems:
Midterm Exam 2
Maria A. Amer, Concordia University, Electrical & Computer Engineering
March 15th, 2016
Q1
(25 marks)
Convolution and LTI systems:
a) Compute the output y(t) of an LTIsystem with the input x(
ELEC242
Sample Final Exam
CT Signals and Systems
Instructions for Examination
This is a closed book exam.
Standard type calculator may be used.
Cellular phones are not allowed.
Questions have equal weight.
Parts a and b of questions have equal weight
ELEC242
ContinuousTime Signals and Systems
FULL NAME:
ID NUMBER:
Nick Name (maximum 8 characters):
If you provide a nick name, your grades will be announced using that nick
name, otherwise your ID number will be used.
=
Instructions for Examination
This
ELEC242W
ContinuousTime Signals and Systems
FULL NAME:
ID NUMBER:
Nick Name (maximum 8 characters):
If you provide a nick name, your grades will be announced using that nick
name, otherwise your ID number will be used.
=
Instructions for Examination
Th
ELEC242/U ContinuousTime Signals and Systems:
Midterm Exam 1
M.A. Amer, Concordia University, Electrical & Computer Engineering
February 4, 2016
Q1
(20 marks)
Simplify the following expressions.
a) y(t) = t cos (2t) (1 t)dt,
2
b) y(t) = (t 3) 4jt , t
2t
ELEC242
ContinuousTime Signals and Systems
FULL NAME:
ID NUMBER:
Nick Name (maximum 8 characters):
If you provide a nick name, your grades will be announced using that nick
name, otherwise your ID number will be used.
=
Instructions for Examination
This
www.concordia.ca
ELEC 242
ContinuousTime Signals and Systems
Rastko Selmic, Ph.D.
Professor
Electrical and Computer Engineering Department
Concordia University
[email protected]
www.concordia.ca/faculty/rselmic.html
1
ELEC 242: Continuous Time
www.concordia.ca
ELEC 242
ContinuousTime Signals and Systems
Rastko Selmic, Ph.D.
Professor
Electrical and Computer Engineering Department
Concordia University
[email protected]
www.concordia.ca/faculty/rselmic.html
1
ELEC 242: Continuous Time
www.concordia.ca
ELEC 242
ContinuousTime Signals and Systems
Rastko Selmic, Ph.D.
Professor
Electrical and Computer Engineering Department
Concordia University
[email protected]
www.concordia.ca/faculty/rselmic.html
1
ELEC 242: Continuous Time
www.concordia.ca
ELEC 242
ContinuousTime Signals and Systems
Rastko Selmic, Ph.D.
Professor
Electrical and Computer Engineering Department
Concordia University
[email protected]
www.concordia.ca/faculty/rselmic.html
1
ELEC 242: Continuous Time
ELEC242/U ContinuousTime Signals and Systems:
Midterm Exam 1
M.A. Amer, Concordia University, Electrical & Computer Engineering
February 4, 2016
Q1
(20 marks)
Simplify theR following
expressions.
t cos (2t) (1 t)dt,
a) y(t) =
2
b) y(t) = (t 3) 4jt
, t
ELEC242
ContinuousTime Signals and Systems
Question 1:
Consider a continuoustime system which has input of x (t ) and output of y (t ) = x 2 (t ) .
a) Is this system linear? Why?
System is not linear as shown below:
Consider x1 (t ) y1 (t ) = x12 (t )
A
W Co ocn otdin Unixet 5in
Engineering and
Computer Science
ELEC242: CT Signal and Systems
Instructor: Amir Asif
Quiz for Assignment # 4
Time Allowed: 15 minutes
Name:
Student ID Number: Email:
Assume that for the CTFT pair x(t) <> X (m) the CTF T 1s giv
ELEC242: CT Signal and Systems
Instructor: Amir Asif
Assignment # 1
Time Allowed: 15 minutes
Name: _Instructors Solution_
Student ID Number: _Email: _
()*
= 2cos
Consider the following CT signal:
/0)*
sin.
+
+
defined in terms of notation introduced in t
COSC3451: Signal and Systems
Instructor: Amir Asif
Quiz for Assignment # 4
Time Allowed: 15 minutes
Name: _Instructors Copy_
Student ID Number: _Email: _
Given the transfer function
H ( s) =
s 2 5 s 84
( s 2 s 35)( s 2 + 9 s + 20)
2
(a)
[2 points]
ELEC 242: CT Signals and Systems
Assignment # 5: Laplace Transform
Problem 6.1
X ( s) =
(b)
x(t )e st dt = e
3 t
0
e st dt =
0
e 3t e st dt + e 3t e st dt =
e (3 s )t dt + e ( s +3)t dt .
0
0
I
II
Integral I reduces to
0
0
e
I=
(3 s ) t
e(3 s )t
1
1
dt =
Solution to Assignment 1
Problem 1: Sketch the following CT signals as function of the independent variable t over the specified
range.
i)
x 2(t ) = sin ( 3 t 8 + 2 ) for ( 1 t 2)
ii)
iii)
x 3(t ) = 5t + 3et for ( 2 t 2)
x5(t ) = cos ( 3 t 4 ) + sin (
ELEC242: CT Signal and Systems
Assignment # 4: CT Fourier Transform
Problem 5.2
(b)
By definition,
X 2 ( ) =
0.5T
0.5e jt dt +
0.5T
1.5T
0.5T
e jt dt = 0.5 (e j )
jt
j 0.5T e j 0.5T
= 0.5
j e
= 0.5
j [ 2 j sin(0.5T ) ]
1
j
1
j
0.5T
0.5T
+ (e j )
j
Assignment 3
ELEC 242 CT Signals and Systems
Problem 4.6
(a)
By inspection, we note that the time period T0 = 2, which implies that the fundamental frequency
0 = 1.
Since the CTFS coefficient a0 represents the average value of the signal, therefore, a0 =
R. Selmic: ELEC 242 ContinuousTime Signals and Systems
Winter 2017
ELEC 242 Final Review
1. For the system below:
x(t)
y(t)
3t
h(t) = e u(t)
a) Use convolution to find y(t) if the input is the step signal.
b) Find y(t) using the Laplace transform if the
R. Selmic: ELEC 242 ContinuousTime Signals and Systems
Winter 2017
ELEC 242 MidTerm Exam (REVIEW)
1. Sketch the following functions of time:
a) x1 (t) = cos(3 t)
b) x2 (t) = cos(3 t + / 2)
Solution:
a)
Sinusoidal function
1
0.8
0.6
0.4
f(t)
0.2
0
0.2

ELEC242W
CT Signals and Systems
Question 1 (5 marks):
Consider a continuoustime LTI system which has impulse response of h(t ) . The signal
x (t ) is applied at the input of this system. Draw the system output y (t ) versus time t .
h (t )
x (t )
2
1
t
ELEC242W
ContinuousTime Signals and Systems
Question 1: Consider a continuoustime system which has input of x(t ) and the output
of y (t ) =
e
2 t + jt
[x(t ) + x(t )]dt .
Evaluate the output signal y (t ) , if the input is x(t ) = (t ) .
Solution 1:
y
Lecture Slides for Signals and Systems
(Version: 20160125)
Michael D. Adams
Department of Electrical and Computer Engineering
University of Victoria
Victoria, British Columbia, Canada
For additional information and resources related to these lecture sli
ContinuousTime Signals and Systems
ELEC 242W, Winter 2016
Department of Electrical and Computer Engineering, Concordia University
Lectures: Tuesdays and Thursdays from 11:45 to 13:00 in room H431
Tutorials: Fridays 11:4513:25 in room H611 or 16:1517:
ELEC242
Assignment 4
CT Signals and Systems
Question 1:
Let x(t ) be a periodic signal as shown below:
x (t ) = 1 + sin t + 2 cos t + cos 2t +
4
a Expand the sinusoidal signals directly in terms of complex exponentials and identify the Fourier
series co
3.4 The input signal x(t) = e_ u(t) is applied to an LTIC system with impulse
response h(t) = euU).
(i) Calculate the output y(t) when 0: 7E 19.
(ii) Calculate the output y(t) when or = [9.
(iii) Intuitively explain why the output signals are different in
ELEC264
Assignment2
SignalsandSystemsI
Question 1) Consider an LTI discretetime system which is characterized by the input/output
1 2
relationship of y[n] = x[n k ] . Find the impulse response of the system and then using
3 k =0
convolution sum evaluate
ELEC264
Assignment1
SignalsandSystemsI
Question 1) Find the even and odd components of the following signals:
a) x(t ) = e 2t cos t
xe (t ) =
cfw_
xe (t ) = cos(t )
xo (t ) =
cfw_
cfw_
1
cfw_x(t ) + x(t ) = 1 e 2t cos t + e 2t cos(t ) = 1 e 2t cos t +
ELEC264
Assignment4SignalsandSystemsI
Solution 1)
Part a)
( ) x[n]e
X e j =
+
jn
= e j 4 + e j 2 + e j 2 e j 4 = 2 cos 2 + 2 j sin 4
n =
Part b)
N = 10 , 0 =
ak =
1
N
2
=
10 5
x[n]e jk (2 / N ) n =
n =< N >
1 j
e
10
6
k
5
+ 2e
7
k
5
j
+ 3e
j
8
k
5
+