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Page 1: Scanned by CamScanner - Purdue Universityelgamala/ECE301-S18/Exam1sol.pdfScanned by CamScanner 518 E C E 301 M idT erın I P ro f A ly El 2G a m a l 1 th Febru a ry 2018 P r o ble

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Page 2: Scanned by CamScanner - Purdue Universityelgamala/ECE301-S18/Exam1sol.pdfScanned by CamScanner 518 E C E 301 M idT erın I P ro f A ly El 2G a m a l 1 th Febru a ry 2018 P r o ble

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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

9 T 断 琳 环 比

Ļ

。 三 、

'

'

、 。

0 = ) W . = ) ţ ı- ı

飞互 日 环 目

s{Ĵ h o ľ r Ĺo d kc/

ミ臥 ん翔 呐公 ロ龙口文ニ a

Page 3: Scanned by CamScanner - Purdue Universityelgamala/ECE301-S18/Exam1sol.pdfScanned by CamScanner 518 E C E 301 M idT erın I P ro f A ly El 2G a m a l 1 th Febru a ry 2018 P r o ble

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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

\ L) 3 m w A (ı m O u i]uÝu k ÝmNU \ k Ýaıyoe IA 80

入学 8旧

悯 · 工

ı,

◆ h

( ķ )

x {n \

.

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Page 5: Scanned by CamScanner - Purdue Universityelgamala/ECE301-S18/Exam1sol.pdfScanned by CamScanner 518 E C E 301 M idT erın I P ro f A ly El 2G a m a l 1 th Febru a ry 2018 P r o ble

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3 e

Page 6: Scanned by CamScanner - Purdue Universityelgamala/ECE301-S18/Exam1sol.pdfScanned by CamScanner 518 E C E 301 M idT erın I P ro f A ly El 2G a m a l 1 th Febru a ry 2018 P r o ble

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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)

O S I 5 5 » 4 5 t

Page 7: Scanned by CamScanner - Purdue Universityelgamala/ECE301-S18/Exam1sol.pdfScanned by CamScanner 518 E C E 301 M idT erın I P ro f A ly El 2G a m a l 1 th Febru a ry 2018 P r o ble

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Page 8: Scanned by CamScanner - Purdue Universityelgamala/ECE301-S18/Exam1sol.pdfScanned by CamScanner 518 E C E 301 M idT erın I P ro f A ly El 2G a m a l 1 th Febru a ry 2018 P r o ble

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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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Page 10: Scanned by CamScanner - Purdue Universityelgamala/ECE301-S18/Exam1sol.pdfScanned by CamScanner 518 E C E 301 M idT erın I P ro f A ly El 2G a m a l 1 th Febru a ry 2018 P r o ble

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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