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5 18 E C E 3 0 1 M id T e r ın I P r o f A ly E l G a m a l 12 th F e b r u a ry , 2 0 18
P r o b le m 1 [2 0 p o in t s] C o n sid e r a D is c r e te T im e s ig n a l e j. ° "
a W h ic h is a h ig h e r fr e q u e n c y b e tw e e n h ).
- o r ĹLT.- î ? W h a t is th e fu n d a m e n ta l
p e r io d in b o th c a s e s ?
b W h a t v a lu e o f o g iv e s th e h igh e s t fr e q u e n c y fo r a d is c r e te s ig n a l? S k e tc h th e c o r r e
s p o n d in g s ig n a l
c If m.
- 5 1 ?r, is th is s ig n a l p e r io d ic ? If y e s
, ñ n d th e fu n d a m e n ta l p e r io d If n o
, ju s tĺ fyy o u r a n s w e r
0 l0 ) fţ W . + E = ) N *
= g
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、
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s{Ĵ h o ľ r Ĺo d kc/
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5 1 8 E C E 3 0 1 M id T e r m I P r o f A ly E 1 G a m a l 12 1h F e b r u a r y , 2 0 18
p r o b le m 2 [2 o p o in t s ] T h e o u tp u Ĺ a ţ tim e'.
' Is o b ta in e d b y a c c u m u la tin g th e v a lu e s o f
th e in p u t fr o m'
o o' to
'
n + 2 '
1 W h a t is th e im p u ls e r e s p o n s e ?
2 M ï h a t is y [n ] w h e n th e in p u t to th e s y s te m is x [ · ] - u [, : ] u [n + 3]?
N o te : u [n ] in d ic a te s u n it s te p
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3 e
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5 18 E C E 3 0 1 M id T e r m I P r o f A 1y E 1 G a m a l 12 th F e b r u a r y , 2 0 18
P r o b le m 4 [2 0 p o in 七 s ]
F ig u r e 1 : x (t)
a F o r x (ţ ) in fig u r e 1,
sk e tc h 3 z ( 2 6 + 3)
国
O S I 5 5 » 4 5 t
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5 18 E C E 3 0 1 M id T e r m I P r o f A ly E 1 G a m a l 1 2 th F e b r u a r y , 2 0 1 8
P r o b le m 5 [2 o p o in t s ] S k e tc h th e e v e n a n d o d d p a r t o f th e s ig n a l (t) g iv e n in F ig u r e 3
F ig u r e 3 : x (t)
\
Ļ
Į
ı
7
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5 18 E C E 3 0 1 M id T e r m I P r o f A 1y E 1 G a m a l 1 2 th F e b r u a r y , 20 18
(P r o b le m 6 c o n tin u e d )
2 D e t e r m in e if e a c h o f th e fo llo w in g s y s te m s is in v e r tib le If it is,
c o n st r u c t th e in v e r s e
s y s te m If iĹ is n o t, fin d tw o in p u t s ig n a ls ţ o th e s y s te rn th a t h a v e s a m e o u tp u t
b u [ · ] ー x [n + S] · [n + 4j
rĻ \ =
ţ e 马\田 ニ
& O T ţ · 5 yLLI = a a t - S
ıóċ b ļ s ) >Ĺk ) フ ł8 01 + 5)
9