![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYDynULg1YLuw0gLeGjqqzo5X4gyLOy0OBifwfRLMKPn5NP9V-SdqpGE9JyMQl9n08yh7ITDa4Gu-Cdu30YnLlSia1-6HNiC2oKc2ofLn7Gdbj2ZYEicQv-nKOhWh0FLlL1qtFM8F9bEVr/s640/Transformasi+Z.jpg)
Kompetensi dasar dan indikator
1 Kompetensi Dasar
Setelah mengikuti praktikum ini, mahasiswa mampu:
- Memahami dan menganalisis sinyal menggunakan Transformasi Z menggunakan Matlab.
2 Indikator
1. Memahami dan menganalisis sinyal menggunakan Transformasi Z dengan menggunakan Matlab .
- Mahasiswa berhasil membuat sourcode untuk menganal isis sinyal menggunakan Transformasi Z menggunakan Matlab.
Dasar Teori
a. Z-Transform
Persamaan matematis z-transform ditunjukkan pada Persamaan 11.1
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEib7tzeEgDYqLzXP9EyPFVnN5hgZtKSrIgFcEarA1jA30VNs4j9CH8UGFvIiYCSEgWrDStjp2BWRkF2sm3f200HlVIDJ4mIhiMmAFFAs1VdofDGi0UIeyVvRMgwOs1j-ZPzoUoFD_SRbpj4/s320/h+134.jpg)
Untuk menentukan z-transform pada Matlab dengan mengetik perintah berikut
>> syms n
>> f = sin(n);
>> ztrans(f)
>> f = sin(n);
>> ztrans(f)
output
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivGlFnBhTlh_EGV13QndsLMlt06T1EuY56ilH-zi5JLeJUzRDaixrfVGXOalWhrRT3_LRXBjkV4IuGY2O_gi9MnVgwtlLiZYYciFvE-QDFQ8dMcGSQZ_EL1YrMNZyfTyApU7fSVt6Bvj6K/s320/1.png)
b. Inverse Z-Transform
Persamaan matematis inverse z-transform ditunjukkan pada Persamaan 11.2
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhp4Q7WUxsEZaPUgq4XFHc9xFP5wfU19fEMPaZETbiAEzXENHMMS_fa4wUoe6Hli1qntqKzJb686dX07ZAbxAPLuCZEcwsZi297uABJptZ11GdbSl_dGM6oc5MXQ-yI8WvLE2RWNE5KvBSO/s320/h+136.jpg)
Untuk menentukan inverse z-transform pada Matlab dengan mengetik perintah berikut
>> syms z
>> f = 2*z/(z-2)^2;
>> iztrans(f)
>> f = 2*z/(z-2)^2;
>> iztrans(f)
output:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiMR0UfXKyyl9wx4FqToTz-IAhYv6QjmWQbEov0t-uVGi8Vqi8EnYPyJvIHOdPnQ7UyLn8ByMXPX4Vawt-wX4sK_UUP0ochUitmSrKLxvtYAdW3cGNSGUAwIqQ31ja0V99kho8D1nD7vYs/s320/1.png)
Langkah Praktikum
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0F2UFXrHe7v5L1YwmWOCeuLbtjSYt3wXhwHsv1lVEV3yNSe8CW46EpOfBMwUDZ122zqybiyaGw0IudhcpnHKi3e0h2csuHA3OI7x82n9Zao9KFFCFQgkdT9ND1tYKjIsL_NmaDcWcGVKh/s320/h+138.jpg)
Ekpresikan fungsi trsnfer-z di dalam bentuk pangkat z-1 berikut ini
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7uFIUXmFH1USDShm2lFcPo58vjt9vClEwB8uwP44_WK7hWAU7GbUkEzoI4ex8GeLQduMecWj2qVYizINCOouLvhSdRhGcWK6YLUKlQCn1kEKqhtdY8xIUiXTMYPNcgMTx-3gcc3DXrU2F/s320/h+139.jpg)
2. Buatlah program pada Matlab untuk menentukan bentuk ekspansi pecah parsial seperti dibawah ini.
B=[0;6;34;0]; %koef. numerator N(z)
A=[1;-7;31;-25]; %koef. denominator D(z)
[R,P,K]=residuez(B,A) %Hitung partial fraction expansion
A=[1;-7;31;-25]; %koef. denominator D(z)
[R,P,K]=residuez(B,A) %Hitung partial fraction expansion
3. Cobalah lihat nilai-nilai R, P dan K dari perintah diatas, apakah nilainya seperti berikut ini
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgai6V5GBfWSiXeTddLMt9WPmVvuSBvuOZBJpHCpQnzF5eAfHwBQv_hNzy-BKLy5kN6qlpZgokgLVLvt0IEL0F9bk096ms8dyVSw-EujRvhioTBuiAd1Ulb27qJIHENG6j24g_EmDBH3ubX/s320/12222224.png)
Latihan
1. Tentukan inverse z -transform dari fungsi berikut ini
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjie7pMIiGnTGxoCHgcucSdQo7OL4espDycpbL67ZHA2gJDO627YHhANGSL0NWR-ZotK_ygbnh4udDUYWYe31grsfEYWz46qGC9aJmj_CLRuExLQeD6PhOpaf1PhzPw8maW1e7Q37LiasNL/s320/h+140.jpg)
A.
syms z
F = (z*(2*z-1))/((z-1)*(z+0.5));
iztrans(F)
F = (z*(2*z-1))/((z-1)*(z+0.5));
iztrans(F)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh51ux_u1TjfqFvZmCFHgoC3z8kkwEf3xjxnSFfa8iVb-iw-wd5VY0fLWrLxfPP-taAYXLvBUvoTewHI4Q3KyASyQzkoDH_15ea9Egg5hpuGwVvISNsRrdYCsG6DCkmmRvxwLnuRpueC9dQ/s320/12222224.png)
B.
syms z
F = 1/((z-1)*(z+0.5));
iztrans(F)
F = 1/((z-1)*(z+0.5));
iztrans(F)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtQZtuA9jzuMM7YcKqDfMulIV5f-lsZy2PrLV0HU5s4SWCqFIf0cTA9PJXuMnU6pBJWvqG6_T8dpsO1MKHBec9gWkhIVG2ZX3np44XVXq710UNbmnefzLWmFdaFt6DrisL11XSZULzKEfG/s320/12222224.png)
C.
syms z
F = 9/((z-1)*(z+0.5)^2);
iztrans(F)
F = 9/((z-1)*(z+0.5)^2);
iztrans(F)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVsrBoiVbwaKodKx8WL-nojbgn0LCFK_gntXbEOXexxX0aBvMSDeHCG2FFH79TNmn8tzsIWodHOOnCosaMNLuA8cFBPZCQzYFx1resclNplSgvgcdHthSOBDbbVDZcx3JuH6qALY7y8xuq/s320/12222224.png)
D.
syms z
F = ((5*z)*(z-1))/(z^2-1.6*z+0.8);
iztrans(F)
F = ((5*z)*(z-1))/(z^2-1.6*z+0.8);
iztrans(F)
Output
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJEV5cdyAUH1GmTU9iidjZnM_rxtl60nYgoGbPAvqa_LhPTIRHvHHE4jTY464bdpPS16gWJdh0kjnEVUzJAH72YA1yC3NAlcFva5scKLTcFm9DVTIgxqw8c3QDg9oAO3gtukseM9LIJgp5/s320/Untitled-1.jpg)
2. Tentukan z-transform dari fungsi berikut ini
Jawab
1.
syms z
F=(z*(2*z-1))/((z-1)*(z+0.5));
iztrans(F)
F=(z*(2*z-1))/((z-1)*(z+0.5));
iztrans(F)
output
Catatan Kuliah
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlJ16Ilh6L-WFwoMCP8zJGxQVfvN84TAlERefanGWXdhK2bCLZQ-7Z5jeLORbqoQ4e58i1numja2LexMt3phcQiY_akyUu4devVEdDqfCVA3hxo0__QbfngCd4dqsCisqG6UVnkiQ-7ja0/s640/12222224.png)
latihan 1
syms n a
x =a^n;
z=ztrans(x)
x =a^n;
z=ztrans(x)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbHLzjHOqP6swFFeTAdBcj5Sjw6YKF6etcY8z7sR96t99YO1-IYVAPFA7W2xHENYQAIn9WvqSYGmrI2Ht3PylK410HmONHWqMkeJnQpxUA8382MhzpYGgHq1VbTVMflS3hmeLfmTKa08at/s320/1.png)
latihan 2
syms n a
x = -a^n;
z=ztrans(x)
x = -a^n;
z=ztrans(x)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAmk43FFXNrblbkuWHw1_RicYEAoP5w4lC7pxxJrK4L8gEiWpkArXu58c-09bgy4OwFOiT3Kf2jHUuWmWkv8WdhfNycsaCd6syjKAwZohaCzhyphenhypheny_lb9tiIKuU3ehzsQ-mXIw2M8Azoa7Cy/s320/12222224.png)
latihan 3
syms n a
x = n*a^n;
z=ztrans(x)
x = n*a^n;
z=ztrans(x)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3WuYfI1xByxNbZiFj8xN-uE1FJt-Q8Uy3baGHVEXgrtUmoXFz9tNK_YT5kIr1K1yFyzLEIUyGCH_k1YjpO15JB91jjqBuIa0mi3dkDMBP-lAckyvH7mj4zoV-Vm-yJ_wz3xdjF4v1hpVV/s320/1.png)
latihan 4
syms n a
x = -n*a^n;
z=ztrans(x)
x = -n*a^n;
z=ztrans(x)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8Vsy03yG0cOyafnpwC-MBoKfBoy0-CYWhWkL-vHZn5h0hsU88WOPH6uExfaiFe3vCVAITfHmT38r4FuA6QcQXaz2yYDIUcyKoHs9Zd3BlMp_9Ok7ObFH6Kj8IG6D0ZdyLvPIZ5drzSLBr/s320/12222224.png)
Latihan 5
syms n w
x = cos(n*w);
z=ztrans(x)
x = cos(n*w);
z=ztrans(x)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkNtob_SJ5ujVerkh7kZAgbKmIyRBUJZeiGIHi4q1g_qRc8AGUgazoQwnpbPDZ9x4u2RZIHyzGZcbPiDDkH-6vXH0J_odLKx2yAkjOm2JQ3aVzMaKfamQnrclpxJtonaJcj7ARgC72yzXK/s320/1.png)
Latihan 6
syms n w
x = sin(n*w);
z=ztrans(x)
x = sin(n*w);
z=ztrans(x)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDOImS44xVbVfqufbJ6Y5CXI09hVE3EFR3_VsMvycPbkwMBCXakgleZCWpeOz1bKog__WVjxsggIRPj__hAR5A8WFMX9CfAIcQWfUxZAJkI9ptDOqq8zw8qSwssg7skr_IhZMSSMV0tx7G/s400/1.png)
Latihan 7
syms a n w
x = (a^n) *cos(n*w);
z=ztrans(x)
x = (a^n) *cos(n*w);
z=ztrans(x)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTRPbgODeSam-xtg1wUdm6koYkHrt1POdX7xYkoL6pvil_lYb09vWjchGY36NhqYRHvTYNU0bINsoU0whD06n3GBhS1zn-Jqv-mB_BDSVLoRFs3uow2RLupSMGrHv9sELDgNINHtjoy5fZ/s320/1.png)
Latihan 8
syms a n w
x = (a^n) *sin(n*w);
z=ztrans(x)
x = (a^n) *sin(n*w);
z=ztrans(x)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio1_gpuYEk96vd266QsU9WHTa6qnlY1zd1ji9kN9bjTnomL_LN-UJg7WkOpoLbHBbhLWFz2WgMBU1CLAwekJYnaJ3MFHw4UIZTJWF35hs6XUB6S5Gk_5yCdtaTv5w5WKxKlfwSfU_ujAf3/s320/12222224.png)
keterangan
un menyatakan posisi atau menandakan mulai , tidak dimakukan dalam rumus
u(n) berarti mulai dari posisi
-u -1 berartimulai dari 1
Link:
https://www.coursehero.com/file/47708655/009-transformasi-Zpdf/
https://yulisun.staff.telkomuniversity.ac.id/files/2016/06/009_transformasi-Z.pdf
NB :
Download laporan di Halaman Daftar Isi
Download laporan di Halaman Daftar Isi