3 sinyal waktu diskrit
TRANSCRIPT
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Review Sinyal dan Sistem
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Berapa periode sampling?
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SINYAL DAN SISTEM WAKTU DISKRITGembong Edhi Setyawan
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SINYAL DAN SISTEM WAKTU DISKRIT
• Sinyal Waktu Diskrit
• Sistem Waktu Diskrit
• Analisis Sistem Waktu Diskrit• Persamaan Beda (Difference Equation)
• Implementasi Sistem Waktu diskrit
• Korelasi Sinyal Waktu Diskrit
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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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Fungsional (Functional Representation)
lainnyan
n
n
n x
,0
2,4
3,1,1
)(
Tabel (Tabular Representation)
n
x(n)
… - 2 -1 0 1 2 3 4 5 …
… 0 0 0 1 4 1 0 0 ---
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Deret (Sequence Representation)
Deret dengan durasi tak terbatas
,0,0,1,4,1,0,0)( n x
,0,0,1,4,1,0)( n x
Deret dengan durasi terbatas
1,4,0,5,2,1,3)( n x
1,4,1,0)( n x
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SINYAL-SINYAL DASAR
Unit impulse sinyal
Unit step signal
Unit ramp signal
Exponential signal
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Unit impulse signal
0,00,1)(
nnnδ
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Unit step signal
0,0
0,1
)( n
n
nu
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Unit ramp signal
0,0
0,
)( n
nn
nur
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Exponential signal (a nyata)
nan x )(
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Exponential signal (a kompleks)
n jnn jner rean x
θθ )()(
θ jrea
)sin(cos)( n jnr n x n θθ
)()()sincos)(
n x jn xnr jnr n x
I R
nn
θθ
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10
cos)9,0(cos)( n
nr n x nn
R
πθ
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10sin)9,0(sin)(
nnr n x nn
I
πθ
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nnn xr n An x
er n x
n
n jn
θφ
θ
)()()()(
)(
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KLASIFIKASI SINYAL
Sinyal energi
Sinyal daya
Sinyal simetris (sinyal genap) Sinyal antisimetris (sinyal ganjil)
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Sinyal Energi dan Sinyal Daya
n
n x E 2
)(Energi dari sinyal x(n)
Bila E terbatas (0 < E < ) x(n) = sinyal energi
N
N n N
n x N
P 2
)(12
1limDaya dari sinyal x(n)
N
N n
N n x E 2
)( N N E N P 12
1lim
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
n x N
PDaya dari sinyal x(n)
P terbatas :
Sinyal periodik = sinyal daya
Bila x(n) adalah sinyal periodik :
)2sin()( N f An x oπ N
k f o
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Sinyal Simetris (Genap) )()( n xn x
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Sinyal Antisimetris (Ganjil)
)()( n xn x
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Bila x(n) adalah sinyal sebarang :
)]()([2
1)( n xn xn xe
)()]()([21)( n xn xn xn x ee
xe(n) adalah sinyal genap
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)]()([2
1)( n xn xn xo
)()]()([2
1)( n xn xn xn x oo
xo (n) adalah sinyal ganjil
)()]()([2
1
)]()([
2
1)()(
n xn xn x
n xn xn xn x oe
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OPERASI-OPERASI SINYAL
Time delay/advance
Folding
Time Scaling (Down-sampling)
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Time Delay/Advance
)k n(x
)n(xTD)n(y 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
)()()( n xn xFDn y
)()1()1()1(
)0()0()0(
)()()(
n x x x y
x x y
n xn xFDn y
dilipat
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)2n(x))2(n(x
)]n(x[TD)n(yTD)n(y
)n(x)n(xFD)n(y
2
122
1
digeser kekanan 2
dilipat
kemudian
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Time Scaling
)()( n xn y µ
)6(x)3(y
)4(x)2(y
)2(x)1(y)2(x)1(y
)0(x)0(y
)n2(x)n(y
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Contoh-Soal 1
Diketahui suatu sinyal diskrit yang didefinisikan sebagai :
lainnyan,0
3n0,1
1n3,3
n1
)n(x
a). Gambarkan x(n)
b). Gambarkan setelah dilipat lalu digeser kekanan 2
c). Gambarkan setelah digeser kekanan 2 lalu dilipat
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-4 -3 -2 -1 0 1 2 3 4 5
lainnyan,0
3n0,1
1n3,3
n1
)n(x
a)
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-4 -3 -2 -1 0 1 2 3 4 5
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
)n(x)n(xFD)n(y1
)n(x
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-5 -4 -3 -2 -1 0 1 2 3 4 5 6
-3 -2 -1 0 1 2 3 4 5 6
)2n(x)n(xTD)n(y 22
)n(x)n(y1
b)
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-4 -3 -2 -1 0 1 2 3 4 5
-2 -1 0 1 2 3 4 5 6 7
)2n(x)n(xTD)n(y 23
)n(x
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-2 -1 0 1 2 3 4 5 6 7
-5 -4 -3 -2 -1 0 1 2
)2n(x))2n((x)2n(xFD)]n(y[FD)n(y 34
)2n(x)n(y3
c)
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Contoh-Soal 2
Diketahui suatu sinyal diskrit seperti terlihatdi bawah ini :
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)?
-3 -2 -1 0 1 2 3 4 5 6
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-3 -2 -1 0 1 2 3 4 5 6
-6 -5 -4 -3 -2 -1 0 1 2 3
)n(x
)n(x
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-5 -4 -3 -2 -1 0 1 2 3 4 5
-5 -4 -3 -2 -1 0 1 2 3 4 5
)n(x)n(x2
1)n(xe
)n(x)n(x2
1)n(xo
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Contoh-Soal 3
Gambarkan sinyal-sinyal berikut :
)2n()2(x)1n()1(x)2n()2(x
)k n(x)k (x)n(x)e
)2n()n(x)n(x)d
}0,1,3,2,1{)n(x),n()n(x)n(x)c
)1n(u)n(u)n(x)b
)3n(u)n(u)n(x)a
2
2k
5
4
3
2
1
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-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
)n(u
)3n(u
)3n(u)n(u)n(x1
Unit step
Pulsa
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-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
)n(u
)1n(u
)n()1n(u)n(u)n(x2
Unit step
Unit impuls
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-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
}0,1,3,2,1{)n(x
)n(
)n()0(x)n(3)n()n(x)n(x 3
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-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
)n(x
)1n(
)1n()1(x)1n()n(x)n(x4
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-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
)n(x
)2n()n(x
2
2k
5 )k n()n(x)n(x
)n()n(x )1n()n(x
)2n()n(x
)1n()n(x
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TUGAS
Bagilah 1 kelas dalam 10 kelompok
Buatlah ulasan (.doc) dan file presentasi(.ppt) dari buku Discrete-Time SignalProcessing, 2nd, Oppenheiem
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