# FE 1314 S1

```COLLEGE OF ENGINEERING
PUTRAJAYA CAMPUS
FINAL EXAMINATION
SEMESTER I 2013 / 2014
PROGRAMME
: Bachelor of Electrical and Electronics Engineering
(Honours)/Bachelor of Electrical Power Engineering
(Honours)
SUBJECT CODE
: EEEB233
SUBJECT
: Signals and Systems
DATE
: October 2013
TIME
: 3 hours
INSTRUCTIONS TO CANDIDATES:
1.
This paper contains SIX (6) questions in SEVEN (7) pages.
2.
3.
4.
Write answer to each question on a new page.
THIS QUESTION PAPER CONSISTS OF 7 PRINTED PAGES INCLUDING THIS
COVER PAGE.
EEEB233, Semester I 2013/2014
Question 1 (15 marks)
(a).
Two discrete-time signals x1[n] and x2[n] described below are input into a
linear time invariant system.
[ ]
(
If the output of the system is [ ]
)
[ ]
(
[ ]
[ ],
)
i) Show that y[n] is periodic.
[2 marks]
ii) Determine the fundamental frequency ω of y[n].
[2 marks]
(b).
Given the discrete time signal x[n] as shown in Figure 1:
Figure 1
i) Determine and sketch the odd parts of the discrete time signal x[n].
[2 marks]
ii) Draw the discrete time signal x[3n+2].
(c).
[2 marks]
Given a system with y[n]  x[n  2]  x[2  n] . Determine if the system is
(i) Causal
[2 marks]
(ii) Time invariant
[3 marks]
(iii) BIBO stable
[2 marks]
Page 2 of 7
EEEB233, Semester I 2013/2014
Question 2 (15 marks)
(a).
A continuous time signal ( )
( ) is an input into a Linear Time
Invariant system of which the impulse response h(t) is shown as
( )
{
Compute the output, y (t ) of the system above using convolution in
time-domain.
[9 marks]
(b).
Given a causal LTI system described by
d 2 y (t )
dy (t )
4
 3 y(t )  2 x(t )
2
dt
dt
Examine whether the system is stable. You are NOT allowed to use any
transform methods.
[6 marks]
Page 3 of 7
EEEB233, Semester I 2013/2014
Question 3 (15 marks)
The periodic signal ( ) with T0 = 1&micro;sec and A = 3 volts shown Figure 2a is input into
an LTI system. The LTI system consisting of a resistor R =1 kΩ connected in series
with a capacitor C = 1 nF is shown in Figure 2b. Determine the following:
(a)
The third harmonic component of the signal ( ).
[7 marks]
(b)
The value of the Fourier Series coefficients for the third harmonic component
of the output signal ( )
[8 marks]
Figure 2a
R = 1 kΩ
C = 1 nF
Figure 2b
Page 4 of 7
EEEB233, Semester I 2013/2014
Question 4 (20 marks)
(a)
Determine the output response, ( ) of the LTI system described by the
differential equation below if the input to the system is
( )
( )
( )
( )
( )
( )
( )
[8 marks]
(b)
A satellite receiver consists a linear time invariant system which uses a time
delay T shown in Figure 3 with the purpose of suppressing external interference
signals. This receiver is being used near a gold mine which has machineries
generating unwanted interference signals with frequencies of 1 MHz and 2
MHz.
The time delay can be constructed from 3 possible different materials
i) Ceramic, T = 0.8 &micro;s ii) Mica, T= 0.16 &micro;s iii) Carbon T = 0.12 &micro;s
Evaluate and propose the most suitable choice of the 3 given materials for use in
the receiver such that it is able to suppress the interference signals?
[12 marks]
Figure 3
Page 5 of 7
EEEB233, Semester I 2013/2014
Question 5 (15 marks)
(a).
Determine the discrete-time Fourier transform of the signal below:
[ ]
[
]
[
]
[5 marks]
(b).
Given a discrete-time LTI system with input signal, x[n] and impulse response,
h[n] as given below:
[ ]
(
)
[ ]
[ ]
(
)
[ ]
Using Fourier transform, determine the output, [ ]
[5 marks]
(c).
Suppose the impulse response of an LTI system is:
[ ]
( )
[ ]
( )
[ ]
Determine the difference equation that describes this system.
[5 marks]
Page 6 of 7
EEEB233, Semester I 2013/2014
Question 6 (20 marks)
(a)
The Laplace Transform Xs  of a continuous-time signal x t  is given as
below:
X s  
(i).
s 1
,  1  Res  2
s s2
2
Sketch the pole-zero pattern of
X s  and its region of convergence.
[4 marks]
(ii).
Determine the signal x t  .
[6 marks]
(b)
Given a discrete-time signal xn  as below,
n
n
1
1
xn     un     u n  1
 3
2
(i).
Determine the z-transform,
X z  and its region of convergence (ROC).
[6 marks]
(ii).
Sketch the pole-zero pattern of
X z  in b(i) and its region of
convergence.
[4 marks]
-END OF QUESTION PAPER-
Page 7 of 7
```