sinyal diskrit baru

7/26/2019 Sinyal Diskrit Baru

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SINYAL DAN SISTEM WAKTU DISKRIT

Sinyal Waktu Diskrit

Sistem Waktu Diskrit

Analisis Sistem Waktu DiskritPersamaan Beda (Dieren!e E"uati#n$

Im%lementasi Sistem Waktu diskrit

K#relasi Sinyal Waktu Diskrit


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SINYAL WAKTU DISKRIT

Re%resentasi Sinyal

Sinyal&sinyal Dasar

Klasiikasi Sinyal

'%erasi%erasi %ada Sinyal


3/42

REPRESENTASI SINYAL

raik (ra%)i!al Re%resentati#n$

*un+si#nal (*un!ti#nal Re%resentati#n$

Ta,el (Ta,ular Re%resentati#n$

Deret (Se"uen!e Re%resentati#n$


4/42

raik (ra%)i!al Re%resentati#n$

n = integer (bilangan bulat) - < n < xa(t) x(n) = xa(nT), T = perioda sampling

x(n) = sinyal ke-n


5/42

*un+si#nal (*un!ti#nal Re%resentati#n$

==

=

lainnyan

n

n

nx

,0

2,4

3,1,1

)(

Ta,el (Ta,ular Re%resentati#n$

n

x(n)

- 2 -1 0 1 2 3 4 !

0 0 0 1 4 1 0 0 ---


6/42

Deret (Se"uen!e Re%resentati#n$

"eret dengan durasi tak terbatas

{ } ,0,0,1,4,1,0,0)( =nx

{ }

,0,0,1,4,1,0)( =nx

"eret dengan durasi terbatas

{ }1,4,0,!,2,1,3)( =nx

{ }1,4,1,0)( =nx


7/42

SINYAL&SINYAL DASAR

Unit im%ulse sinyal

Unit ste% si+nal Unit ram% si+nal

E-%#nential si+nal


8/42

Unit im%ulse si+nal

==0,0

0,1)(n

nn


9/42

Unit ste% si+nal

=

0,0

0,1)(n

nnu


10/42

Unit ram% si+nal

=

0,0

0,)(n

nnnur


11/42

E-%#nential si+nal (a nyata$

n

anx =)(


12/42

E-%#nential si+nal (a k#m%leks$

njnnjn erreanx === )()(

j

rea=

)sin(#os)( njnrnx n +=

)()()sin#os)(

nxjnxnrjnrnx

IR

nn

+=+=


13/42

10#os)$,0(#os)(

nnrnx nnR

==


14/42

10sin)$,0(sin)(

nnrnx nnI

==


15/42

nnnxrnAnx

ernx

n

njn

====

=

)()()()(

)(


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KLASI*IKASI SINYAL

Sinyal ener+i

Sinyal daya

Sinyal simetris (sinyal +ena%$

Sinyal antisimetris (sinyal +an.il$


17/42

Sinyal Ener+i dan Sinyal Daya

== n nxE 2

)(%nergi dari sinyal x(n)

&ila % terbatas (0 < % < ) x(n) = sinyal energi

=

+=

N

NnN

nxN

P 2

)(12

1lim"aya dari sinyal x(n)

==N

Nn

N nxE 2)( NN

EN

P12

1lim+=

&ila ' terbatas dan 0 x(n) = sinyal daya


18/42

x(n ) = x(n) = perioda

=

=1

0

2)(

1 N

n

nxN

P"aya dari sinyal x(n)

' terbatas *

+inyal periodik = sinyal daya

&ila x(n) adala sinyal periodik *

)2sin()( NfAnx o=N

kfo=


19/42

Sinyal Simetris (ena%$ )()( nxnx =


20/42

Sinyal Antisimetris (an.il$

)()( nxnx =


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&ila x(n) adala sinyal sebarang *

)-()(.21)( nxnxnxe +=

)()-()(.2

1

)( nxnxnxnx ee =+=

xe

(n) adala sinyal genap


22/42

)-()(.2

1)( nxnxnxo =

)()-()(.2

1)( nxnxnxnx oo ==

xo (n) adala sinyal gan/il

)()-()(.

2

1

)-()(.2

1)()(

nxnxnx

nxnxnxnx oe

=

++=+


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'PERASI&'PERASI SINYAL

Time delay/ad0an!e

*#ldin+ Time S!alin+ (D#1n&sam%lin+$


24/42

Time Delay/Ad0an!e

[ ]

)kn(x

)n(xT")n(y k

=

=

[ ]

)n(x

)2(x)31(x)1(y)3(x)30(x)0(y

)3n(x)n(xT")n(y 3

==

==

==

di+eser ke kanan 2

)n(x

)3(x)21(x)1(y

)2(x)20(x)0(y)2n(x)n(x.T")n(y 2

=+=

=+=+==

di+eser ke kiri 3


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*#ldin+

[ ] )()()( nxnxFDny ==[ ]

)n(x

)2(x)31(x)1(y

)3(x)30(x)0(y

)3n(x)n(xT")n(y 3

==

==

==

dili%at

[ ] )()(")(


26/42

[ ]

[ ]

)2n(x))2(n(x

)-n(x.T"

)n(yT")n(y

)n(x)n(x")n(y

2

122

1

+==

=

=

==

di+eser kekanan3

dili%at

kemudian


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Time S!alin+

)()( nxny =

)(x)3(y

)4(x)2(y

)2(x)1(y

)2(x)1(y

)0(x)0(y

)n2(x)n(y

==

==

=

=

t + l 1


28/42

onto-+oal 1

"iketaui suatu sinyal diskrit yang dideinisikan sebagai *

+

=lainnyan,0

3n0,1

1n3,3

n1

)n(x

a) 5ambarkan x(n)

b) 5ambarkan setela dilipat lalu digeser kekanan 2

#) 5ambarkan setela digeser kekanan 2 lalu dilipat

n


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&4 &2 &3 &5 6 5 3 2 4 7

+

=

lainnyan,0

3n0,1

1n3,3

n1

)n(x

a$


30/42

&4 &2 &3 &5 6 5 3 2 4 7

&7 &4 -2 &3 &5 6 5 3 2 4 7 8

[ ] )n(x)n(x0")n(y1 ==

)n(x


31/42

&7 &4 -2 &3 &5 6 5 3 2 4 7 8

&2 &3 -5 6 5 3 2 4 7 8

[ ] )2n(x)n(xT")n(y 22 ==

)n(x)n(y1 =

,$


32/42

&4 &2 &3 &5 6 5 3 2 4 7

&3 &5 6 5 3 2 4 7 8 9

[ ] )2n(x)n(xT")n(y 23 ==

)n(x


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&3 &5 6 5 3 2 4 7 8 9

&7 &4 &2 &3 &5 6 5 3

[ ] )2n(x))2n((x)2n(x")n(y.")n(y 34 +====

)2n(x)n(y3 =

!$

onto +oal 2


34/42

onto-+oal 2

"iketaui suatu sinyal diskrit seperti terliatdi ba6a ini *

a) 5ambarkan bagian genap dari x(n)=xe(n)

b) 5ambarkan bagian gan/il dari x(n)=xo(n)

#) 7umlakan kedua bagian ini, apaka sama dengan x(n)8

&2 &3 &5 6 5 3 2 4 7 8


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&2 &3 &5 6 5 3 2 4 7 8

&8 &7 &4 &2 &3 &5 6 5 3 2

)n(x

)n(x

[ ]1


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&7 &4 &2 &3 &5 6 5 3 2 4 7

&7 &4 &2 &3 &5 6 5 3 2 4 7

[ ])n(x)n(x2

1)n(xe +=

[ ])n(x)n(x2

1)n(xo =

onto +oal 3


37/42

onto-+oal 3

5ambarkan sinyal-sinyal berikut *

)2n()2(x)1n()1(x)2n()2(x

)kn(x)k(x)n(x)e

)2n()n(x)n(x)d

90,1,3,2,1:)n(x),n()n(x)n(x)#

)1n(u)n(u)n(x)b)3n(u)n(u)n(x)a

2

2k

!

4

3

2

1

+++++=

=

=

==

==

=


38/42

&8 &7 &4 &2 &3 &5 6 5 3 2 4 7 8

)n(u

)3n(u

)3n(u)n(u)n(x1 =

Unit ste%

Pulsa


39/42

&8 &7 &4 &2 &3 &5 6 5 3 2 4 7 8

)n(u

)1n(u

)n()1n(u)n(u)n(x2 ==

Unit ste%

Unit im%uls


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&8 &7 &4 &2 &3 &5 6 5 3 2 4 7 8

90,1,3,2,1:)n(x =

)n(

)n()0(x)n(3)n()n(x)n(x3 ===


41/42

&8 &7 &4 &2 &3 &5 6 5 3 2 4 7 8

)n(x

)1n(

)1n()1(x)1n()n(x)n(x4 ==


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)n(x

)2n()n(x +

=

=2

2k

! )kn()n(x)n(x

)n()n(x )1n()n(x

)2n()n(x

)1n()n(x +

sinyal diskrit baru

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