PENGOLAHAN SINYAL DIGITAL. Modul 4. Transformasi Z

Transkripsi

1 PENGOLHN SINYL DIGITL Mdul. Trsfrmsi Z

2 Ctet Overview TZ utu fugsi esesil usl d ti usl, ROC, Zer Ple, TZ fugsi imuls, TZ fugsi siusidl Overview ITZ : Pech Prsil d Itegrsi Ktur, miulsi ITZ berdsr rertyy, ROCy usl d ti usl, fugsiy. cth : ITZ fugsi lgritm f d TZ fugsi /.

3 Ltr Belg Dmis f reresetti Dmi- discrete time : Sequece, imulse resse, ersm bed Dmi- : Freq. resse, sectrl reresetti Dmi- : Oertr, d le-er bil sutu sus sulit diech d sutu dmi tertetu, m trsfrmsi e dmi yg li mudh meyelesiy.

4 Ctet Trsfrmsi-Z Lgsug Sift-sift Trsfrmsi-Z Trsfrmsi-Z Rsil Trsfrmsi-Z Bli Trsfrmsi-Z Stu Sisi

5 TRNSFORMSI-Z LNGSUNG Defiisi : Cth :.,, b., 5,, 7, 5, 0, 5 7, 0,

6 Cth : Jwb: Tetu trsfrmsi Z dri beber siyl di bwh ii: 0, c. 0, b b c.

7 Cth : Jwb: Tetu trsfrmsi Z dri siyl u :,dim... 0 ROC u :, ROC u

8 Cth : Jwb: Tetu trsfrmsi Z dri siyl u ROC u :,dim ROC u :,

9 TBEL FUNGSI DSR TZ

10 SIFT-SIFT PROPERTY TZ

11 SIFT-SIFT TRNSFORMSI-Z Liierits :, :, ROC u ROC u Tetu trsfrmsi Z dri siyl : : 6 5 ROC ROC Z u b b Cth 5: u

12 SIFT-SIFT TRNSFORMSI-Z Pergeser :, R ROC Z u Tetu trsfrmsi Z dri siyl Jwb: Z 0 0 Cth 5: u :, R ROC Z Z u

13 SIFT-SIFT TRNSFORMSI-Z Time Reversl :, R ROC Z u Tetu trsfrmsi Z dri siyl Jwb: Cth 6: u :, R ROC u

14 SIFT-SIFT TRNSFORMSI-Z Diferesisi dlm dmi Tetu trsfrmsi Z dri siyl Cth 7: d d u R ROC u :, d d d d u u

15 SIFT-SIFT TRNSFORMSI-Z Kvlusi tr du siyl Tetu vlusi tr d deg : Cth 8: * liy 0, 5 0,,, ,,0,0,0,0,, *

16 TRNSFORMSI Z RSIONL Ple d Zer Ple : hrg-hrg = i yg meyebb = Zer : hrg-hrg = i yg meyebb = 0 N 0 M 0 N N M M b b b b D N Fugsi Rsil N N N M M M N M Z b b b b b D N 0 b 0

17 N d D lim N N N M M M N M Z b b b b b D N 0 b 0 b D N M M M N N M M N G

18 Tetu le d er dri,5,5 Jwb: 0,75 0,75,5 0,75 : 0,75 0 : Ple Zer Cth 9:

19 ] ][ [ j j * : 0 : j j Ple Zer Tetu le d er dri Jwb: Cth 0:

20 TRNSFORMSI -Z BLIK Defiisi trsfrmsi bli d j C di lur bil dlm C di bil d f d d f j C 0,,! Terem residu Cuchy :

21 Essi deret dlm d - Tetu trsfrmsi- bli dri Jwb: , 6, 8 5, 7,, Cth :

22 Essi frsi-rsil d tbel trsfrmsi- K K K K,5,5,5 Tetu trsfrmsi- bli dri Jwb: Cth :

23 ,5 ] [ u,5 0,5,5

24 Ple-le berbed semu N N N N

25 Cth Sl 8.7 Tetu er-stte resse dri sutu sistem LTI yg medt iut = u d diyt leh ersm bed : y 6y 8y Jwb: Y 6 Y 8 Y Y Y

26 8 8 5 Y Y Y Y 0 Y 0 Y ]u 0 [ y s

27 d du le yg semu N N d d

28 Cth Sl 8.8 Tetu trsfrmsi-z bli dri : Jwb:

29 d d d d ]u [

30 Ple mles * * * * * * * * * * * * * * b b

31 * Re j Im Re j Im Re b * Re * Re j Im Re j Im Re * Re * [Re j Im][Re j Im] Re Im * * * [Re j Im][Re j Im] [Re j Im][Re j Im] Re Re Im Im * [Re j Im][Re j Im] [Re Re Im Im] j[re Im Re b * * Re* Im]

32 Cth Sl 8.9 Tetu trsfrmsi-z bli dri : Jwb: b b b Re Re Re Re b Re* Re* Re Im

33 Im Im Re Re Re j Im Im j jim] [ * j Im Im Re* j j j j * *

34 j j j j j5 j5 0,707e j 0,707e j si 5 0,707 5 cs 0,707 jsi 5 5 cs j0,707 jsi 5 5 cs 0,707 jsi 5 5 cs j0,707 jsi 5 5 cs 0,707 j 0,707e j 0,707e j5 j5

35 Defiisi : TRNSFORMSI-Z STU SISI 0 Cth Sl 8.0 Tetu trsfrmsi Z stu sisi dri beber siyl disrit di bwh ii. b.,,,, 5, 5, 7, 7, 0, 0, c. d. 0,,, 5,, 7, 5, 0, 7, 0,

36 Jwb: , 7, 5,,, , 7, 5,,, b , 7, 5,,, 0, c , 7, 5,, d.

37 Cth Sl 8. Tetu trsfrmsi Z stu sisi dri beber siyl imuls di bwh ii. b. c ,, 0 0 Jwb:. b c

38 Time Dely Cth Sl 8. [ Tetu trsfrmsi Z stu sisi dri = - dim = u ] Jwb: u

39 Time dvce Cth Sl 8. [ 0 Tetu trsfrmsi Z stu sisi dri = + dim = u ] Jwb: u 0 0

40 Cth Sl 8. Tetu utut dri sutu sistem LTI Lier Time Ivrit yg diyt leh ersm bed : y y y,5 9,5 y 8,5 y 7,5 deg iut = 0 Jwb: y y i Y [Y [Y y ] y y ] 0

41 7 7,5 8,5 8,5 Y y y y ] [ Y 0 ] y y [Y ] y [Y Y 7 7 Y

42 7 7 Y 7 Y 6,5 6,5 7 Y 6,5 6,5 Y i 6,5 y

43 Cth Sl 8.5 Tetu utut dri sutu sistem LTI yg medt iut = u d diyt leh ersm bed : y 6y 8y y y Jwb: Y 8 8 [Y [ 6 [Y y ] y ] y 8 [ ] 5 ] Y [ 6 8 ] [5 8 8 ]

44 ] 8 8 [5 ] 8 6 [ Y ] 8 6 [ Y Y Y Y

45 Y

46 Y Y ]u [ y