KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
Department of Systems Engineering
MAJOR EXAM I
CISE 315(111)
Signals and Systems
Name: _______________________________
01
ID: ___________________Section: ________
Instructor: Dr. M. Al-Dhaifallah
Question
1
2
3
4
5
6
Total
Points
4
4
3
4
3
2
20
Grade
Instructions:
1. Do not start before you are told to do so.
2. Write clearly. Show details of your work.
1
[Question 1]
Sketch and label Carefully each of the following signals, where x(t) and x[n] are given below
A) x(2t+2).
B) x(1 -3t).
C) x[n-2] .
D) x[4-n]
A)
C)
B)
D)
2
[Question 2]
A. Show that if x[n] is an odd signal, then

 x[n]  0
n 
B. Show that if x1[n] is an odd signal and x2[n] is an even signal, then x1[n]x2[n] is an odd signal.
C. Consider the signal y[n] given below
Find the signal x[n] such that Ev{x[n]} = y[n] for n > 0, and Od{x[n]} = y[n] for n < 0.
3
4
[Question 3]
The following Table contains the input-output relations for several continuous-time and discrete-time
systems, where x(t) or x[n] is the input. Indicate whether the property along the top row applies to each
system by answering yes or no in the appropriate boxes. Do not mark the shaded boxes.
y(t), y[n]
A. (2+sin(t))x(t)
B. x(2t)
Memoryless
Linear
Time-Invariant
Causal
Invertible
Stable

C.
 x[k ]
k 
D. Consider the signals
 2 t 
 16 t 
x  t   cos 
  2sin 

 3 
 3 
y  t   sin  t 
Show that z(t) = x(t)y(t) is periodic, and write z(t) as a linear combination of harmonically related
complex exponentials. That is, find a number T and complex numbers Ck such that
z  t    Ck e jk  2 / T t
k
5
D.
6
[Question 4]
A. Determine the discrete-time convolution of x[n] and h[n] for the following case.
B. Determine the discrete-time convolution of x(t) and h(t) for the following case
A.
B.
7
8
[Question 5]
A. Consider the three discrete-time signals shown in the following Figure
You may have noticed a similarity between the convolution operation and multiplication, but they
are not equivalent. Verify that
( x  y ) w  x  ( y w)
B. Find the combined impulse response of the LTI system in the following Figure. Recall that
x(t)*h(t)*h-1(t) = x(t).
A.
9
B.
10
11