bab 2 sinyal diskrit
TRANSCRIPT
![Page 1: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/1.jpg)
SINYAL WAKTU DISKRIT
Representasi Sinyal Sinyal-sinyal Dasar Klasifikasi Sinyal Operasi-operasi pada Sinyal
![Page 2: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/2.jpg)
REPRESENTASI SINYAL
Grafik (Graphical Representation) Fungsional (Functional Representation) Tabel (Tabular Representation) Deret (Sequence Representation)
![Page 3: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/3.jpg)
Grafik (Graphical Representation)
n = integer (bilangan bulat) - < n <
xa(t) x(n) = xa(nT), T = perioda sampling
x(n) = sinyal ke-n
![Page 4: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/4.jpg)
Fungsional (Functional Representation)
lainnyan
n
n
nx
,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 ---
![Page 5: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/5.jpg)
Deret (Sequence Representation) Deret dengan durasi tak terbatas
,0,0,1,4,1,0,0)( nx
,0,0,1,4,1,0)( nx
Deret dengan durasi terbatas
1,4,0,5,2,1,3)( nx
1,4,1,0)( nx
![Page 6: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/6.jpg)
SINYAL-SINYAL DASAR
Unit impulse sinyal Unit step signal Unit ramp signal Exponential signal
![Page 7: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/7.jpg)
Unit impulse signal
0,0
0,1)(
n
nn
![Page 8: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/8.jpg)
Unit step signal
0,0
0,1)(
nn
nu
![Page 9: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/9.jpg)
Unit ramp signal
0,0
0,)(
nnn
nur
![Page 10: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/10.jpg)
Exponential signal (a nyata)
nanx )(
![Page 11: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/11.jpg)
Exponential signal (a kompleks)
njnnjn erreanx )()(
jrea
)sin(cos)( njnrnx n
)()(
)sincos)(
nxjnx
nrjnrnx
IR
nn
![Page 12: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/12.jpg)
10cos)9,0(cos)(
nnrnx nn
R
![Page 13: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/13.jpg)
10sin)9,0(sin)(
nnrnx nn
I
![Page 14: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/14.jpg)
nnnxrnAnx
ernxn
njn
)()()()(
)(
![Page 15: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/15.jpg)
KLASIFIKASI SINYAL
Sinyal energi Sinyal daya Sinyal simetris (sinyal genap) Sinyal antisimetris (sinyal ganjil)
![Page 16: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/16.jpg)
Sinyal Energi dan Sinyal Daya
n
nxE2
)(Energi dari sinyal x(n)
Bila E terbatas (0 < E < ) x(n) = sinyal energi
N
NnN
nxN
P2
)(12
1limDaya dari sinyal x(n)
N
NnN nxE
2)(
NN
EN
P12
1lim
Bila P terbatas dan 0 x(n) = sinyal daya
![Page 17: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/17.jpg)
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 oN
kfo
![Page 18: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/18.jpg)
Sinyal Simetris (Genap) )()( nxnx
![Page 19: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/19.jpg)
Sinyal Antisimetris (Ganjil)
)()( nxnx
![Page 20: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/20.jpg)
Bila x(n) adalah sinyal sebarang :
)]()([2
1)( nxnxnxe
)()]()([2
1)( nxnxnxnx ee
xe(n) adalah sinyal genap
![Page 21: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/21.jpg)
)]()([2
1)( nxnxnxo
)()]()([2
1)( nxnxnxnx oo
xo (n) adalah sinyal ganjil
)()]()([2
1
)]()([2
1)()(
nxnxnx
nxnxnxnx oe
![Page 22: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/22.jpg)
OPERASI-OPERASI SINYAL
Time delay/advance
Folding Time Scaling (Down-sampling)
![Page 23: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/23.jpg)
Time Delay/Advance
)kn(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
![Page 24: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/24.jpg)
Folding
)()()( nxnxFDny
)n(x
)2(x)31(x)1(y
)3(x)30(x)0(y
)3n(x)n(xTD)n(y 3
dilipat
![Page 25: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/25.jpg)
)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
![Page 26: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/26.jpg)
Time Scaling
)()( nxny
)6(x)3(y
)4(x)2(y
)2(x)1(y
)2(x)1(y
)0(x)0(y
)n2(x)n(y
![Page 27: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/27.jpg)
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
![Page 28: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/28.jpg)
-4 -3 -2 -1 0 1 2 3 4 5
lainnyan,0
3n0,1
1n3,3
n1
)n(x
a)
![Page 29: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/29.jpg)
-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
![Page 30: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/30.jpg)
-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)
![Page 31: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/31.jpg)
-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
![Page 32: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/32.jpg)
-2 -1 0 1 2 3 4 5 6 7
-7 -6 -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)
![Page 33: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/33.jpg)
Contoh-Soal 2
Diketahui suatu sinyal diskrit seperti terlihat di 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
![Page 34: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/34.jpg)
-3 -2 -1 0 1 2 3 4 5 6
-6 -5 -4 -3 -2 -1 0 1 2 3
)n(x
)n(x
![Page 35: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/35.jpg)
-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
![Page 36: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/36.jpg)
Contoh-Soal 3
Gambarkan sinyal-sinyal berikut :
)2()2()1()1()2()2(
)()()()
)1()()()
}0,1,3,2,1{)(),()()()
)1()()()
)3()()()
2
25
4
3
2
1
nxnxnx
knxkxnxe
nnxnxd
nxnnxnxc
nununxb
nununxa
k
![Page 37: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/37.jpg)
-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
![Page 38: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/38.jpg)
-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
![Page 39: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/39.jpg)
-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(x3
![Page 40: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/40.jpg)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
)n(x
)1n(
)1n()1(x)1n()n(x)n(x4
![Page 41: Bab 2 Sinyal Diskrit](https://reader035.vdocuments.us/reader035/viewer/2022081716/552b51f94a795953588b461e/html5/thumbnails/41.jpg)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
)n(x
)2n()n(x
2
2k5 )kn()n(x)n(x
)n()n(x )1n()n(x
)2n()n(x
)1n()n(x