EEE2035F: Signals and Systems I
1. (5 marks) Consider the two signals below:
1
Class Test 2
22 April 2013
0
1
x(t)
1
t
2
0
y(t)
1
2
The convolution v(t) = x(t) y(t) is as follows:
c
v(t)
a
Name:
Specify a, b, and c.
Student number:
Information
The test i
EEE2035F: Signals and Systems I
1. (5 marks) Find the complex exponential Fourier series representation of the periodic
signal below:
Class Test 2
(1)
16 April 2010
8 7 6 5 4 3 2 1
SOLUTIONS
Signal has period T = 6 so 0 =
2
6
=
3
(1)
1
x(t)
2
3
4
5
6
7
8
EEE2035F: Signals and Systems I
1. (10 marks) Plot the signals given below. Where appropriate, assume that s(t) is the signal
1
Class Test 1
s(t)
0
11 March 2011
1
(a) x1 (t) = cos(t).
(b) x2 (t) = cos(t)u(t + 1).
(c) x3 (t) =
Name:
(d) x4 (t) =
(e) x5 (t
EEE2035F: Signals and Systems I
1. (5 marks) Find the complex exponential Fourier series representation of the periodic
signal below:
Class Test 2
(1)
16 April 2010
8 7 6 5 4 3 2 1
Name:
Student number:
Information
The test is closed-book.
This test has
EEE2035F: Signals and Systems I
Class Test 2
16 April 2010
Name:
Student number:
Information
The test is closed-book.
This test has four questions, totalling 20 marks.
Answer all the questions.
You have 45 minutes.
1. (5 marks) Find the complex expone
EEE2035F: Signals and Systems I
1. (5 marks) Sketch the following signals, where u.t / is the unit step function:
(a) x1 .t / D u.t /
u.t
Class Test 1
12 March 2010
(d) x4 .t / D u.t
/
(e) x5 ./ D u.t
1/
(b) x2 .t / D u.2t /
/.
(c) x3 .t / D u.2.t
1/
SOLU
EEE2035F: Signals and Systems I
1. (5 marks) Sketch the following signals, where u.t / is the unit step function:
(a) x1 .t / D u.t /
u.t
Class Test 1
(b) x2 .t / D u.2t /
12 March 2010
(d) x4 .t / D u.t
/
(e) x5 ./ D u.t
/.
Name:
Student number:
Informat
1. (5 marks) The signal
x.t /
1
EEE2035F: Signals and Systems I
Class Test 2
t
2
1
0:5
0:5
1
2
has a Fourier series representation
1
X
x.t / D
24 April 2009
ck e j k t ;
kD 1
where
8
<1=2
ck D
: 1 sin.k=2/
SOLUTIONS
kD0
otherwise:
k
(a) Plot the magnitude
1. (5 marks) The signal
x.t /
1
EEE2035F: Signals and Systems I
Class Test 2
t
2
x.t / D
1
X
8
<1=2
ck D
: 1 sin.k=2/
k
1
2
ck e j k t ;
kD0
otherwise:
(a) Plot the magnitude and phase of the Fourier series coefcients corresponding to
k D 5 to 5.
Student
EEE2035F: Signals and Systems I
Class Test 2
24 April 2009
Name:
Student number:
Information
The test is closed-book.
This test has four questions, totalling 20 marks.
Answer all the questions.
You have 45 minutes.
1. (5 marks) The signal
1
x.t /
t
2
EEE2035F: Signals and Systems I
1. (5 marks) The periodic signal
Class Test 2
.
x.t /
1
.
2
5 May 2008
1
1
2
t
has a Fourier series representation
Name:
x.t / D
Student number:
with
Information
The test is closed-book.
This test has four questions, tota
EEE2035F: Signals and Systems I
1. (10 marks) Plot the signals given below. Where appropriate, assume that s(t) is the signal
1
Class Test 1
s(t)
1
0
11 March 2011
t
3
(a) x1 (t) = cos(t).
(b) x2 (t) = cos(t)u(t + 1).
SOLUTIONS
(c) x3 (t) =
(d) x4 (t) =
d
EEE2035F: Signals and Systems I
Class Test 2
21 April 2011
Name:
Student number:
Information
The test is closed-book.
This test has four questions, totalling 20 marks.
Answer all the questions.
You have 45 minutes.
1. (5 marks) suppose x(t) is the sig
EEE2035F: Signals and Systems I
Class Test 2
22 April 2013
Name:
Student number:
Information
The test is closed-book.
This test has four questions, totalling 20 marks.
Answer all the questions.
You have 45 minutes.
1. (5 marks) Consider the two signal
EEE2035F: Signals and Systems I
1. (5 marks) For the following signals, y(t) = h(t) x(t):
2
Class Test 2
x(t)
1
1
t
y(t)
b
t
2
0
23 April 2012
c
h(t)
1
a
1
t
2
SOLUTIONS
Find the values of a, b, and c, justifying all answers.
From the properties of convol
EEE2035F: Signals and Systems I
1. (5 marks) For the following signals, y(t) = h(t) x(t):
2
Class Test 2
x(t)
1
1
t
0
23 April 2012
2
t
2
Find the values of a, b, and c, justifying all answers.
Name:
Student number:
Information
The test is closed-book.
EEE2035F: Signals and Systems I
Class Test 2
23 April 2012
Name:
Student number:
Information
The test is closed-book.
This test has four questions, totalling 20 marks.
Answer all the questions.
You have 45 minutes.
1. (5 marks) For the following signa
EEE2035F: Signals and Systems I
1. (5 marks) suppose x(t) is the signal below
1
x(t)
Class Test 2
2
21 April 2011
1
1
0
and let
2
p(t) =
SOLUTIONS
t
3
(t nT )
n=
be an impulse train with T = 5.
(a) Plot p(t) in the time domain.
(b) Find and plot y(t) = p(
EEE2035F: Signals and Systems I
1. (5 marks) suppose x(t) is the signal below
1
x(t)
Class Test 2
2
21 April 2011
1
1
0
and let
(t nT )
p(t) =
n=
Name:
be an impulse train with T = 5.
Student number:
(b) Find and plot y(t) = p(t) x(t).
(a) Plot p(t) in th
EEE2035F: Signals and Systems I
1. (6 marks) Suppose x.t / is the signal below:
1
Class Test 1
t
0
20 March 2009
2
Sketch the following:
(a) ya .t / D x. 2
SOLUTIONS
1
(b) yb .t / D
(c) yc .t / D
t/
d
x.t / (generalised
dt
Rt
1 x./d
derivative)
(d) yd .t
EEE2035F: Signals and Systems I
1. (6 marks) Suppose x.t / is the signal below:
1
Class Test 1
t
0
20 March 2009
2
Sketch the following:
(a) ya .t / D x. 2
(b) yb .t / D
Name:
1
(c) yc .t / D
t/
d
x.t / (generalised
dt
Rt
1 x./d
derivative)
(d) yd .t / D
EEE2035F: Signals and Systems I
1. (10 marks) Given
Class Test 1
22 March 2007
x.t / D
sketch
8
t
<
1
:
0
(a) x.t /
(b) y1 .t / D x.2t C 1/
Name:
(c) y2 .t / D x.2
(d) the generalised derivative y3 .t / D
Student number:
Information
The test is closed-bo
EEE2035F: Signals and Systems I
Class Test 2
19 May 2006
Name:
Student number:
Information
The test is closed-book.
This test has four questions, totalling 20 marks.
There is an information sheet attached at the end of this paper.
Answer all the quest
EEE2035F: Signals and Systems I
Class Test 2
19 May 2006
Name:
Student number:
Information
The test is closed-book.
This test has four questions, totalling 20 marks.
There is an information sheet attached at the end of this paper.
Answer all the quest
EEE2035F Class Test
1. (10 marks) A LTI system has an impulse response
h.t /
1
28 April 2006
0
t
2
Find the response of the system to the input
Name:
Student number:
1
Information
The test is closed-book.
This test has three questions, totalling 30 mark
EEE2035F Class Test
28 April 2006
Name:
Student number:
Information
The test is closed-book.
This test has three questions, totalling 30 marks.
There is a bonus question for 5 marks.
Answer all the questions.
You have 45 minutes.
1. (10 marks) A LTI