signals and systems
DESCRIPTION
Final Exam QuestionsTRANSCRIPT
![Page 1: Signals and Systems](https://reader036.vdocuments.pub/reader036/viewer/2022081802/563db83f550346aa9a91ecdc/html5/thumbnails/1.jpg)
7/17/2019 Signals and Systems
http://slidepdf.com/reader/full/signals-and-systems-568bf72284744 1/3
MEH226 Signals and SystemsFinal Exam (2014-2015 Summer)
26.08.2015
Name, Surname : 1 (10) 2 (20) 3 (25) 4 (15) 5 (40) Total
Student NumberSignature
::
Q1 1A. For the given8
( ) sin 4 ( 0.25)2 ( 0.25)
x t t t
compute and draw the spectrum of ( ) ( ).cos400 y t x t t . 15
() = 82 4 ∗( − 0.25) = 164 4 ∗( − 0.25) = 164 ∗ ( − 0.25)
( ) = [164]. = 2 ∏ − = 16, 2 = 4 ===> = 8, = 2 ( ) = 4∏ 8
() = ().400
↔ ( ) = 12 ( ) ∗ [( − 400) + ( + 400)]
( ) = 2∏ − 4008 + 2∏ + 4008
400π
Y(jw)
-404π 396π 404πw
-400π -396π
400π
Arg(Y(jw))
-404π 396π 404πw
-400π -396π
π
-π
π
-π
2
1B. Find and draw the spectral energy density of ( ) y t . 10
() = |( )| = 2 ∏ − 4008 + ∏ + 400
8 . 2 ∏ − 400
8 + ∏ + 400
8 ∗
() = 4 ∏ − 4008 + ∏ + 4008 /
400π
S(w)
-404π 396π 404πw
-400π -396π
4
1C. Find the energy of ( ) y t . 10
= 12 ()
= 12 4
+ 12 4 = 12 (32 + 32) = 32
![Page 2: Signals and Systems](https://reader036.vdocuments.pub/reader036/viewer/2022081802/563db83f550346aa9a91ecdc/html5/thumbnails/2.jpg)
7/17/2019 Signals and Systems
http://slidepdf.com/reader/full/signals-and-systems-568bf72284744 2/3
( ) z t 6 6( )6 6
w w H jw
( ) 2.cos4 . ( 0,5 )n
v t t t n
( ) 2 ( 0 .5) x t t
( ) y t
2A. Find and draw the spectrum of ( )v t . 10
() = 2 4 ( − 0.5) = 2 4 2 ( − 0.5) = 2 (2) ( − 0.5) = 2 ( − 0.5)
() = 2 ( − 0.5) ↔ ( ) = 2 − 20.5
= 2 = 20.5 = 4 ⎭
( ) = 8 ( − 4)
4
V(jw)
w4 8 8
8
2B. ( ) ? z t 10
() = () ∗ ℎ() = [()] ( ) = ( ). ( ) = 8 [( − 4) + ( + 4) + ( − 8) + ( + 8)] () = 8 4 +8 8
2C. Find and draw of ( )Y jw . 10
() = ()() = (8 4 +8 8) 2 − 12 = 8 4 12 + 8 8 12 2 − 12 = (8 + 8) 2 − 12
() = 32 − 12
( ) = 32
Y(jw)
w
Arg(Y(jw))
2πw
-w/2
-π
32
Q2. The system given on the right
side,
![Page 3: Signals and Systems](https://reader036.vdocuments.pub/reader036/viewer/2022081802/563db83f550346aa9a91ecdc/html5/thumbnails/3.jpg)
7/17/2019 Signals and Systems
http://slidepdf.com/reader/full/signals-and-systems-568bf72284744 3/3
π
V(jw)
w
3π3π
π
-6π -2π 2π 6π
-2/3
-2π2π
-6π
2/3
-/3
/3
Arg[V(jw)]
w6π
3A. Find the frequency response of the LTI system. Is the LTI system causality? Explain.15
( ) = 3 ↔ ℎ() = 3( − 0.5)
ℎ() = 2 (2)3 − 14 = 2 2 14 − 14 = 2 12 − 14 = 4 − 14
ℎ() = ℎ() ∗ ℎ() + ℎ() = 3( − 0.5) ∗ 4 − 14 + 12 + 34 = 12 − 34 + 12 + 34
Nedensellik için ℎ() = 0 < 0 olmalı. Burada ise ikinci terim bunu sağlamadığından sistem nedensel değildir.
( ) = 12 + 12 = 24 34
3B. Find the output signal y t for the given system input signal of ( )V jw . 10
() = 3 2 +
+
6 +
() = 3|(2)| 2 + 3 + ((2)) + |(6)| 6 + 23 +((6))
|(2)| = 24 34 2 = 0
|(6)| = 24 34 6 = 24 3 = −24 = 24
() = 24 6 + 2
3 − = 24 6 −
3
Q4. Find the output ( ) y t when the input signal is 22
( ) 8 sinw j w
V jw e c
and the impulse response LTI systems is
( ) (2 3)h t t . 25
∏ − ↔ 2 ( ) = 8 2 ↔ () = 2 ∏ 4 ∗ ( − 0.5) = 2 ∏ − 0.54
() = () ∗ ℎ() = 2 ∏ − 0.54 ∗ (2 − 3) = 2 ∏ − 0.54 ∗ 12 − 32 = ∏ − 1.5 − 0.54 = ∏ − 24
Q3. The LTI system given on the right side, 12( ) 3.w
j H jw e
,
12 4( ) 2 . (2 ). ( )h t Sinc t t , 3
34
( ) 12 ( )h t t .
+v(t)
h3(t)
y(t)h1(t) h2(t) +