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(ELEC211)[2010](f)midterm~hlchanab^_10302.pdf
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Student Name : ________________________________ Student ID : _______________________
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Answer all questions in this examination paper in the space provided.

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Show all your calculations and steps clearly. No works will be given for unjustified answers.

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This is a close books and close notes exam.

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No note sheet, cheat sheet or draft paper is allowed.

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No use of mobile phones, computers, PDA or calculators is allowed.

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No use of electronic devices with communication capabilities is allowed


-No communications or talking will be allowed during the exam time.
- Students caught cheating will receive zero marks and referred to the university for discipline.
Question Max. Points Points
1 40(+4 bonus)
2 30
3 30
Total 100

Table 3.1, 3.2, 4.1, 4.2 and 5.2 are provided on the last page of this exam paper.
j. j j. j
e + ee . e
Eulers Relation cos= sin=
22 j

Convolution Integral y(t) = x( ) h(t . ) d= h( ) x(t . ) d
. .

Convolution Sum y[n] = x[k] h[n . k] = h[k] x[n . k]
k =. k =.
jk ot 1 . jk t 2
o
CTFS x(t) = ake ak = x(t) e dt o = k =. TT T
jk n 1 . jk n 2
oo
DTFS x[n] = ae a = x[n] e =
kk o k =<N > Nn =<N > N
1
j t . j t
CTFT x(t) = X ( j) ed X ( j) = x(t) e dt
2. . 1 2
j jtj. jn
DTFT x[n] = X (e ) ed X (e ) = x[n] e2 n =.
31 j j 2
cos( / 6) =
cos( / 4) =
cos( / 2) = 0 cos() =.1 e =.1 e = 1 22
11 j . j sin( / 6) = sin( / 4) =
sin( / 2) = 1 sin() = 0 e 2 = je 2 =. j22
Q1a Q1b Q1c
Answer

(2. j10)t
a.Which of the following is the plot of Re{eu(.t)}

0
C. D.

u(-t) means the signal must be 0 for all t>0, which only D satisfies. The positiveness of the real part in the exponent means that the signal is growing with increasing t, or decaying with decreasing t, which matches D as well.
b..Let xt() = tut () +(t.2) be the input to an LTI system with impulse response ht () = ut() .ut( . 2) . y(3), the output at time t=3 equals
A. 1 B. 2
C. 3 D. 4
ANS: 5 (All students got 2 marks)
The impulse response represents the integration of the input over the previous 2 time units. At t=3, the total area under the input from t=1 to t=3 is 5.
c. 4 t2(t. 3)dt= ?
2
A. 0 B. 1
C. 4 D. 9
24 t t.24 (3)
2(3) dt = 32 t. dt = 9
Q1d Q1e Q1f Q1g Q1h
Answer

d. x(t) is as shown below:

Which of the following represents x(2(3.t))?
A. B.

-2

1.5 3.5


A. y[n] = x[n] + 6 B. y[n] = x[n] + n
2
C. y[n] =x[n] D. y[n] = log x[n]
2
A & B do not satisfy zero-input-zero-output. D is logarithmic and nonlinear.
f.Which of the following systems is causal?
A. y(t) = x(.t) B. y(t) = x(t)e3tu(t+1)
.3t
yt 5) (
C. () = ut( . xt +5) D. y(t) = x(t)*eu(t+1) where * represents convolution
B is memoryless and hence causal. W