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VIETNAM NATIONAL UNIVERSITY, HANOIUNIVERSITY OF ENGINEERING AND
TECHNOLOGY
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SOCIALIST REPUBLIC OF VIETNAM
Independence Freedom Happne!!
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E#AMINATION $UESTIONS AND E#ERCISES
%& Co'r!e In(orma)on
- Course title: Signals and Sste!s
- Course I": ELT#$%&
- Nu!'er o( )redits: $%
- Nu!'er o( )redit *ours +Le)La're./: 0& +0#%$/
- resi1uisite: MAT2$3&
- Course grou.: Co!.ulsor Ele)ti4e *& Lec)'rer+!
In(orma)on
Le V' Ha, PhD.
5a)ult o( Ele)troni)s and Tele)o!!uni)ations
Uni4ersit o( Engineering and Te)*nolog
Vietna! National Uni4ersit, Hanoi
*one nu!'er: +$0/ %6&0 3#62 E!ail: *al474nu8edu84n
,& L!) o( $'e!)on! and E-erc!e!
,&%& M'.)p.e/c0oce 1'e!)on!
9uestion 28 *i)* one o( t*e (ollo;ing state!ents is
INCORRECT2)2+t (2
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A8 h(t)=)os( t)
=8 h(t)=e# tu(t2)
C8 h(t)=u(t+2)
"8 h( t)=)os ( t)u(t)
9uestion 2$8 *i)* o( t*e sste!s des)ri'ed ' t*e (ollo;ing
i!.ulse res.onses is)ausali4en t*e La.la)e trans(or! !(s ) o( t*e
(ollo;ing signal:
x (t)=)os(# t)u (t)
"eter!ine t*e signal y (t) i( its La.la)e trans(or! is gi4en
':
%(s)=s#!(s)
Eer)ise 2&&8 >i4en t*e La.la)e trans(or! o( t*e
signal x (t) as (ollo;s:
!(s )= #s
s# +#
"eter!ine La.la)e trans(or! o( t*e (ollo;ing signal:
y (t)=x (% t)
Eer)ise 2&B8 >i4en t*e La.la)e trans(or! o( t*e signal x
(t) as (ollo;s:
!(s )=#s
s#+#
"eter!ine La.la)e trans(or! o( t*e (ollo;ing signal:
y (t)=x (t#)
##
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Eer)ise 2&68 >i4en t*e La.la)e trans(or! o( t*e signal x
(t) as (ollo;s:
!(s )=#s
s#+#
"eter!ine La.la)e trans(or! o( t*e (ollo;ing signal:
y (t)=x (t)dx (t)
dt
Eer)ise 2&8 >i4en t*e La.la)e trans(or! o( t*e signal x
(t) as (ollo;s:
!(s )=#s
s#+#
"eter!ine La.la)e trans(or! o( t*e (ollo;ing signal:
y (t)=etx (t)
Eer)ise 2&38 >i4en t*e La.la)e trans(or! o( t*e signal x
(t) as (ollo;s:
!(s )= #s
s# +#
"eter!ine La.la)e trans(or! o( t*e (ollo;ing signal:
y (t)=# tx(t)
Eer)ise 2B$8 >i4en t*e (ollo;ing La.la)e trans(or! .air:
x (t)=eatu( t) !(s )= 2
s+a
E4aluate t*e unilateral La.la)e trans(or! o( t*e (ollo;ing
signal:
y (t)=eat)os($ t)u(t)
Eer)ise 2B$8 "eter!ine t*e (or)ed and natural res.onses (or t*e
LTI sste! des)ri'ed
' t*e (ollo;ing di((erential e1uation ;it* t*e s.e)i(ied initial
and in.ut )onditions:
dy (t)dt +2$y (t)=2$x ( t) , y ($)=2 , and x (t)=u (t)
Eer)ise 2B28 "eter!ine t*e (or)ed and natural res.onses (or t*e
LTI sste! des)ri'ed
' t*e (ollo;ing di((erential e1uation ;it* t*e s.e)i(ied initial
and in.ut )onditions:
d#y (t)
dt#
+&dy (t)dt
+ By( t)=0x( t)%dx (t)dt
, y ($)=2 , dy (t)
dtt=$=& andx (t)=etu( t)
Eer)ise 2B#8 "eter!ine t*e (or)ed and natural res.onses (or t*e
LTI sste! des)ri'ed
' t*e (ollo;ing di((erential e1uation ;it* t*e s.e)i(ied initial
and in.ut )onditions:
d#
y (t)dt
# +y (t)=Cx (t) , y ($)=$ , dy (t)dtt=$=# and x (t)=etu( t)
Eer)ise 2B%8 "eter!ine t*e (or)ed and natural res.onses (or t*e
LTI sste! des)ri'ed
' t*e (ollo;ing di((erential e1uation ;it* t*e s.e)i(ied initial
and in.ut )onditions:
d#y (t)
dt#
+#dy (t)dt
+&y (t)=dx( t)dt
, y ($)=# , dy (t)
dtt=$=$ and x (t)=u (t)Eer)ise 2B08 "eter!ine t*e ti!e-do!ain
signal )orres.onding to t*e (ollo;ing 'ilateral
La.la)e trans(or!:
!(s )= e
&s
s+# (Re (s)
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!(s )=d
#
ds#( 2s% ) (Re (s)>%)
Eer)ise 2BB8 "eter!ine t*e ti!e-do!ain signal )orres.onding to
t*e (ollo;ing 'ilateral
La.la)e trans(or!:
!(s )=s0
s#+%s+#
(#
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Eer)ise 2668 "eter!ine t*e trans(er (un)tion and t*e i!.ulse
res.onse o( a )ausal
sste! des)ri'ed ' t*e (ollo;ing di((erential e1uation:
d#y (t)
dt#
dy ( t)dt
#y (t)=0x (t)+&dx (t)dt
Appro2ed 34
Un2er!)4 Board
Appro2ed 34
Fac'.)4 Board
Appro2ed 34
Depar)men) Prepared 34
