PENGOLAHAN SINYAL DIGITAL - jusewisman.files.wordpress.com · Representasi Sinyal • Grafik...
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PENGOLAHAN SINYAL DIGITAL
Modul 3.Sinyal Waktu Diskrit
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Content
• Overview Sinyal Waktu Diskrit• Representasi Sinyal• Sinyal‐sinyal Dasar• Klasifikasi Sinyal• Operasi‐operasi pada Sinyal
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Representasi Sinyal
• Grafik (Graphical Representation)• Fungsional (Functional Representation)• Tabel (Tabular Representation)
• Deret (Sequence Representation)
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• Grafik (Graphical Representation)
n = integer (bilangan bulat) ‐ ∞ < n < ∞
xa(t) x(n) = xa(nT), T = perioda sampling
x(n) = sinyal ke‐n
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⎪⎪⎩
⎪⎪⎨
⎧
=−−=−=
=
lainnyannnn
nx
,02,1
2,1,23,1,0,1
)(
• Fungsional (Functional Representation)
• Tabel (Tabular Representation)
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Deret dengan durasi tak terbatas
{ }ΛΛ ,1,2,1,2,1,2,)( −−−=nx
Deret dengan durasi terbatas
{ }1,1,2,1,1,2)( −=nx
• Deret (Sequence Representation)
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Sinyal‐sinyal Dasar
Unit impuls sinyalUnit step signalUnit ramp signalExponential signal
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⎩⎨⎧
≠=
=0,00,1
)(nn
nδ
• Unit impulse signal
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⎩⎨⎧
<≥
=0,00,1
)(nn
nu
• Unit step signal
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⎩⎨⎧
<≥
=0,00,
)(nnn
nr
• Unit ramp signal
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nanx =)(• Exponential signal (a nyata)
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Klasifikasi Sinyal
Sinyal energiSinyal dayaSinyal genap (sinyal simetris)Sinyal ganjil (sinyal antisimetris)
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• Sinyal Energi dan Sinyal Daya
∑∝
∝−=
=n
nxE 2)(Energi dari sinyal x(n)
Bila E terbatas (0 < E < ∝) x(n) = sinyal energi
∑−=
→∝ +=
N
NnNnx
NP 2)(
121limDaya dari sinyal x(n)
∑−=
=N
NnN nxE 2)(
NNE
NP
121lim+
=→∝
Bila P terbatas dan ≠ 0 x(n) = sinyal daya
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x(n + N) = x(n) N = perioda
∑−
=
=1
0
2)(1 N
n
nxN
PDaya dari sinyal x(n)
P terbatas :
Sinyal periodik = sinyal daya
Bila x(n) adalah sinyal periodik :
)2sin()( NfAnx oπ=Nkfo =
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• Sinyal Genap (Simetris)
)()( nxnx =−
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• Sinyal Ganjil (Antisimetris)
)()( nxnx −=−
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Bila x(n) adalah sinyal sebarang :
)]()([21)( nxnxnxe −+=
)()]()([21)( nxnxnxnx ee =+−=−
xe(n) adalah sinyal genap
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)]()([21)( nxnxnxo −−=
)()]()([21)( nxnxnxnx oo −=−−=−
xo (n) adalah sinyal ganjil
)(
)]()([21)]()([
21
)()(
nx
nxnxnxnx
nxnx oe
=
−−+−+=
+
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Operasi‐operasi Sinyal
Time delay (pergeseran waktu) Folding (pencerminan)Time Scaling (skala waktu)
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• Time Delay[ ]
)()()(
knxnxTDny k
−==
[ ]
)n(x)2(x)31(x)1(y)3(x)30(x)0(y
)3n(x)n(xTD)n(y 3
−=−=−=−=
−==
digeser ke kanan 3
)n(x)3(x)21(x)1(y)2(x)20(x)0(y
)2n(x)]n(x[TD)n(y 2
=+==+=
+== −
digeser ke kiri 2
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• Folding
[ ] )()()( nxnxFDny −==[ ]
)(1)1()1(2)1()1(
)()()(1
nxxy
xynxnxFDny
==−=−=
−==
dicerminkan sumbu vertikal[ ]
( )nxnxnx
nxTDnyTDny
)2())2(()]([)()(
2
122
+−=−−−=−=
=
−
−
dicerminkan, kemudiandigeser ke kanan 2 satuan
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• Time Scaling )()( nxny μ=
)4()2()2()1(
)2()1()0()0(
−=−−=−
==
xyxy
xyxy
)2()( nxny =
Contoh :
… dst
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Diketahui suatu sinyal diskrit yang didefinisikan sebagai :
⎪⎩
⎪⎨
⎧≤≤−
−≤≤−−=
lainnyannn
nnnx
,030,1
12,)(
Gambarkan :
a. x(n) b. x(‐n‐2) c. x(‐2n+4)
Contoh Soal 1
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a.Jawab :
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b. Gambarkan
( )( )2)2( +−=−− nxnx
cerminkangeser ke kiri 2 satuan
cerminkan
geser ke kiri 2 satuan
)2( −−nxCara 1. operasi sinyal
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Cara 2. perhitungan
)2()( −−= nxny
( )( ) ( )
0)4()2(0)1()1(2)2()0(1)1()1(1)0()2(
0)1()3(1)2()4(
2325)5(
=−==−==−==−=−−==−
==−==−
==−−−=−
xyxyxyxyxyxyxy
xxy
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c. Gambarkan
( )( )22)42( −−=+− nxnx
cerminkan geser ke kanan 2 satuan
kompresi 2x
geser ke kanan 2 satuan
)42( +− nxCara 1. operasi sinyal
kompresi 2x
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Cara 2. perhitungan
)42()( +−= nxny
( ) ( )
2)2()3(1)0()2(
1241.2)1(
=−=−==
==+−=
xyxy
xxy
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Diketahui suatu sinyal diskrit sebagai berikut :
Contoh Soal 2
a. Gambarkan bagian genap dari x(n)=xe(n)
b. Gambarkan bagian ganjil dari x(n)=xo(n)
c. Jumlahkan kedua bagian ini, apakah sama dengan x(n)?
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[ ])n(x)n(x21)n(xe −+= [ ])()(
21)( nxnxnxo −−=
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+
=)()()( nxnxnx oe =+
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Gambarkan sinyal‐sinyal berikut :
Contoh Soal 3
( ) ( )( ) ( ) ( )( ) ( ) ( )12c.
2b1a.
3
2
1
−−+=−−=
−−−=
nununxnununx.
nunx
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( ) ( )( )( )1nu
1nunxa. 1
+−−=−−−=
( ) ( ) ( )2nununxb. 2 −−=
‐
=
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( ) ( ) ( )1nu2nunxc. 3 −−+=
‐
=