Bab 3: Sinyal dan Sistem di Domain z

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1 BB 3 Sil d Sistm di Dmi B 3: Sil d Sistm di Dmi lis sil d sistm is dirmdh il dil d dmi. Ut it, sil d sistm dirrstsi dlm dmi ii mdi hsil dii t lis. Trsfrmsi d Sil. Dfiisi Trsfrmsi T Blr srt mgthi dfiisi Trsfrmsi dri sil srt dfiisi d grti Rgi f Cvrgc RC, i sh limil. Kws Wt frwrd ivrs Kws Z Z-l sqc limil Z-trsfrm t sil : {} Rgi f Cvrg ROC : r dlh drt t higg m scr mtmtis is rili t trhigg tid lh. Olh s it g is dig dlh ROC T Blr srt mgthi hw t sil rdrsi trts fiit drti, dlh limil rrd trts dg RC slrh idg cli titi trtt. III-

2 BB 3 Sil d Sistm di Dmi {,, 5, 7,, } ROC slrh -l cli, T Blr 3 srt mgthi dri imls d vrsi trgsr sh sml. {,, 5, 7,, } ROC slrh -l cli, δ ROC : slrh -l δ-, > - ROC : slrh -l, cli δ, > ROC : slrh -l, cli T Blr 4 srt mgthi t sil drsi t higg srt RC g ssi gi. Cri Z-trsfrm dri / Jw : {,,,,,, 3, }... III-

3 BB 3 Sil d Sistm di Dmi Igt, il < Scr mm rl, il ; ROC : < ; ROC : >/ t >. T Blr 5 srt mgthi rd RC t sil rdrsi t higg sl di lr ligr, ti-sl di dlm ligr, d misi cici. Kvrgsi dri sil sl d tisl rtm it th hw ilg mls dt dit dlm t rtsi t t lr, misl θ r R Im I m θ R Gmr. Bt lr dri ilg mls. θ r III-3

4 BB 3 Sil d Sistm di Dmi θ c < r θ r θ r r r r r Trm csl : d trm hrs vrg r < r hrs cil, < r < r r I m r R Trm sl < r, r>r, >r Gmr. ROC t trm sl. III-4

5 BB 3 Sil d Sistm di Dmi I m r R Gmr 3. ROC t gi sl. Kl d-d sl d sl d d r < r, m ROC rt cici. Gmr 4. ROC t sil dg gi sl d sl. Cth :, cri ROC : - < III-5

6 BB 3 Sil d Sistm di Dmi III-6 > Ctt. Bil,, > Cth :,, l l Ctt., < - < < trt sm dg slm cli ROC

7 BB 3 Sil d Sistm di Dmi O sidd Gmr 5. ROC t sil g fiit m ifiit.. Ivrsi Trsfrmsi T Blr 6 III-7

8 BB 3 Sil d Sistm di Dmi Ivrs : srt mgrti dfiisi Ivrs trsfrmsi srt r dri trm Cch ctr itgrl. Cch Ctr Itgrl c π, d, π, d, c d c d c c π π c d d.3 Sift-Sift Trsfrmsi T Blr 7 srt mgthi d dt mmft sift liir dri trsfrmsi, trms t mghitg trsfrmsi dri sil cs ω d si ω. Sift Lir: ROC ROC ROC : ROC i III-8

9 BB 3 Sil d Sistm di Dmi Cth : [3-43 ] ROC : > ROC : > ROC : > Z > 3 Z 3Z Hitg. csω. siω Cth : csω csω csω 3 siω siω csω T Blr 8 srt mgthi it rgsr di dmi wt trhd d dt mmft. - Z - ROC : sm dg cli > < III-9

10 BB 3 Sil d Sistm di Dmi III- Cth : lswhr,, Cri rhti : - Di m - - > ROC > hitg lwt cr li cs ω ω ω ω ω > ω ω > ROC: cs cs > ω ω ω ω ω ω ω ω ω ω ω ω

11 BB 3 Sil d Sistm di Dmi si ω ω ω siω csω ROC : > T Blr 9 srt mgthi it sclig di dmi trhd sil di dmi wt d dt mmft. r < < r - r < < r Bti: Z il ROC : r < < r r < / < r r < < r T Blr srt mgthi it tim-rvrsl di dmi wt trhd sil di dmi d dt mmft. ROC : r < <r m ROC : /r < </r Bti : III-

12 BB 3 Sil d Sistm di Dmi Cth : l l l r < - <r - /r < </r ROC : < T Blr srt mgthi it difrsisi di dmi trhd sil di dmi wt d dt mmft. d d [ ] - - Z{} d Z{ } d Cth : ROC : > d. d III-

13 BB 3 Sil d Sistm di Dmi > Cth : > T Blr srt mgthi hw vlsi d sil di dmi wt mghsil rli d sil di dmi, d dt mmft.. Cth : Hitg Di m {, -, }, 5, lswhr w : III-3

14 BB 3 Sil d Sistm di Dmi {, -,,,,, -, } Cr li: liht cth slm * dst. T Blr 3 srt mgthi trm disi wl d mgg. Trm Kdisi wl csl i..,, < lim lim liht tl! Bt Rsil dri Trsfrmsi. Bt Rsil d lt l-zr T Blr 4 srt mgl t hss rsil dri, d mgrti srt dt mcri l d r dri trst. srt dt mmlt l-r trst di idg. Dfiisi : III-4

15 BB 3 Sil d Sistm di Dmi III-5 Zr dri dlh ili-ili di m l dri dlh ili-ili di m rsil, D / Bil d r d D limil, m i i i i G lt : Gmr 6. l d r dilt d -l msig-msig dg lmg d. T Blr 5 Im R rs ls

16 BB 3 Sil d Sistm di Dmi srt dt mcri d rdsr lt l r. Cth : lt l-r dri sil > ROC : > r ; Cth : Gmr 7. Kfigrsi l d r d sh ss. Ut,, lswhr ccls π /... - r - l III-6

17 BB 3 Sil d Sistm di Dmi Gmr 8. Kfigrsi l d r. Sl : Cri Z-trsfrm dri sil dri : Jw: Gmr 9. Kfigrsi l-r dlm gsi. r : ; rcsω l : r ω ; r -ω G r G csω ω r ω r r csω G r csω G r csω ROC > r III-7

18 BB 3 Sil d Sistm di Dmi T Blr 6 srt mmhmi sift sil sl di ws wt it lsi l, mgg ss st l, l gd, d ssg l cml cgt. srt g mgrti hg lsi l dg stilits sistm. Sift ws wt sil sl it lsi l C d <,, > it circl Kss l rl > Gmr. grh sisi l trhd dimi sil. Kss l rl dl > III-8

19 BB 3 Sil d Sistm di Dmi Gmr. grh sisi l gd trhd dimi sil. Kss ssg cml cgt III-9

20 BB 3 Sil d Sistm di Dmi Gmr. grh sisi l gd gt trhd sift dimi sil. Jdi: sil dg l di dlm it circl sll trts mlitd. l dt rigi dc ct rl t sistm stil 3 Trsfrmsi Ut Sistm T Blr 7 srt dt mdfiis fgsi sistm H dri h m hg I/O dri sistm LTI. srt g dt mcri H dri sistm LCCDE scr ct, trms t ss hss ll-r d ll-l. Fgsi Sistm: III-

21 BB 3 Sil d Sistm di Dmi III- H H / Sistm Fgsi h h H Sistm LCCDE: H Kss hss - H ll r, FIR H ll l Cth : Cri H d h dri /- Jw: h H 4 Ivrsi dg Cr rtil Frcti T Blr 8 srt mgrti risi ivrsi trsfrmsi dg cr rtil frcti, i t g rr m g imrr.

22 BB 3 Sil d Sistm di Dmi III- Ivrsi rtil frcti trm stdr, rgtg l d ROC ivrs msig-msig Ivrsi dg rtil Frcti Dfiisi rr il il d < il tid rr is dit t rr irr T Blr 9 srt dt ml ivrsi trsfrmsi dg cr rtil frcti t g rr d mmilii l disti. <... sll rr Cth :,5.5

23 BB 3 Sil d Sistm di Dmi III Ctt.,...,... Cth :.5.5 / / / - / 3 3

24 BB 3 Sil d Sistm di Dmi III-4 T Blr srt dt ml ivrsi trsfrmsi dg cr rtil frcti t g rr d mmilii l g rrd gd. H d d >, csl i.5.5 Cth :.5, ROC >, <.5, t.5< <

25 BB 3 Sil d Sistm di Dmi III-5 Kti > csl -.5 <.5 is csl * ROC.5 < < < ti csl >.5 csl T Blr srt dt ml ivrsi trsfrmsi dg cr rtil frcti t g rr d mmilii sg l cml cgt. Cth : [ ] [ ] r r β β β cs * *

26 BB 3 Sil d Sistm di Dmi III cs π π T Blr srt dt ml ivrsi trsfrmsi d LCCDE mlli rh t dlm t l-r, d mdi mdmsisi dlm r lm trm imrr, sigl rl l, cgt ls, d mltil ls, mdi msigmsig dirss ssi cr msig-msig. > /4-3/4 [/ ] [/4-3/4 /] Dmsisi mltils c ltrtif :

27 BB 3 Sil d Sistm di Dmi 5 Trsfrmsi St Sisi T Blr 3 srt mgthi dfiisi trsfrmsi st sisi srt siftsift d rsm d rd dri is. sift-sift : Tid mmi ifrmsi t < Ui t sil sl ROC sll trir dri sh ligr T Blr 4 srt dt mr sift shiftig dri i tim dl m tim dvcd d mgrti rd dri sift shiftig. Sm Z trsfrm rrtis rl cli sift shiftig Kss. Tim dl III-7

28 BB 3 Sil d Sistm di Dmi III-8 sl il ] [ > Bti : ] [ Z [ l l l dst. Cth : - di m ] [ Z r d Z

29 BB 3 Sil d Sistm di Dmi III-9 Scr ititif : ]... [ } { - > Z Kss. Tim dvcd > Bti : } { l l l Z sdg l l l l l l l l l } { l l l Z Cth : Bil, cri Z {} Jw: ] [ } { Z T Blr 5 srt mgrti sift simtti dri trsfrmsi st sisi. lim lim

30 BB 3 Sil d Sistm di Dmi III-3 limit ist il ROC - mgdg Cth : d h < cri ili st sqc dri H H ROC : Kr < ROC mgdg lim lim T Blr 6 srt dt mr trsfrmsi st sisi d ss slsi dri drt Ficci. Drt Ficci :,,, 3, 5, 8, Cri cls frm : - - Kdisi wl d - [ ] [ ] Ivrsi :

31 BB 3 Sil d Sistm di Dmi III T Blr 7 srt dt mr trsfrmsi st sisi d ss sistm dg disi wl trtt. Tt rss st dri - < dg disi wl - w : [ ] 6 Rss Sistm T Blr 8 srt dt mghitg rss sistm g mmilii H rsil, rdsr lis l d r dri sil it d fgsi sistm, trms mgidtifisi rss trl d frcd rss.

32 BB 3 Sil d Sistm di Dmi III-3 Rss dri sistm g mmilii fgsi-fgsi sistm, g rsil Q B H Bil disi wl, Q B H Bil ls sistm :,,, sil : q, q,, q L q m,, m,,,l Bil tid d r g mmt trdi l-r cclti, m Frcd Rss rss trl L L q Q q Q rl dictt hw f,q Q f,q Zr it r tt trl rss Jdi trl rss r it rss t ili rld. T Blr 9 srt dt mghitg rss sistm g mgdg l rdr gd/.

33 BB 3 Sil d Sistm di Dmi III-33 Kss mltil rdr ls ss srti d scti 3.4., i : mgdg trm l,,,m mgdg trm - l T Blr 3 srt dt mghitg rs sistm g mgdg l-r d disi wl tid l trms mgidtifisi r stt rss d r it rss. isl ditr d d -,, - Cri, H s i s H h LCCDE

34 BB 3 Sil d Sistm di Dmi III-34...,,, i s i i D ' L D q Q ' f dri iitil cditi dlh mgltr rss trl dg mgh mlitd mdi, tti tid d f d frcd rss. T Blr 3 srt mmhmi im dri disi wl d rss. Cth : Cri rss it st Iit : Jw : Rld / 9. π

35 BB 3 Sil d Sistm di Dmi π. 9 / s π / 3 π / [ cs π/3-5. ] Ut i π / 3 π / i csπ/3 87 s i π / 3 π / [ csπ/3 38 ] T Blr 3 srt dt mghitg trsi d std stt rsss dri sistm g mgdg l-r. r < r dcs I this cs r trsit rss Bil l dt lm dc L fr Q q il q < fr dcs trsit rss ti il q fr sisid std stt III-35

36 BB 3 Sil d Sistm di Dmi vr dcs s ss, msti d trs, > cth : Cri trsit d std stt rss dri.5- cs π/4 - rld H l.5.5 H mili H π / 4 mili 6.78 π 8.7 / 4 r fr 8.7 π / π / 4 [ ] 3.56 cs π/4-8.7 rsist 7 lis Stilits Sistm T Blr 33 srt mgrti hg tr disi l-r sistm dg slits d stilits dri sistm, mlli lis RC. Trms di dlm ss l-r cclti, d mltil l d it circl. Kslits III-36

37 BB 3 Sil d Sistm di Dmi h < ROC strir dri sh ligr LTI csl sstm ROC strir dri ligr r <, trms BIBO h < H h H h h H h Jdi il BIBO stl, m d di ROC, t g r. BIBO stil ROC Bil csl ROC strir r Stil ROC > r < sm l hrs d di dlm it circl Cth : 3 4 H Cri ROC dri h gr stil csl c ticsl Jw : Sstms hs ls / & 3. Stil ROC hrs trms it circl, / < < 3 h / III-37

38 BB 3 Sil d Sistm di Dmi III-38. Csl ROC > > 3 h / 3 c. ti csl ROC : <.5 h -/ th sstms is stl * l - Zr Cclltis Cth : Cri it sml rss δ dri sistm rit ii : slsi : H ls /, 6 5 H B 5/ B d r g mgccl - Zrs : H.5 h δ Sstm Sstm

39 BB 3 Sil d Sistm di Dmi III-39 3 trdi cclti Cri rss δ δ H 3 md /3 dit sgi hsil dri l-r ccllti * ltil l l it circl c dgrs Cth : H il U stl ss mltil l : m-, m rd dri l dmits

40 BB 3 Sil d Sistm di Dmi il < tlh stil g rg : digitl sciltrs mrgil stl T Blr 34 srt mgrti stilit tst mrt ti Schr-Ch, d ti t rd. Stilit tst :... rts dri hrs d dlm it circl liht Schr-Ch hl 3! * Stilits t sistm rd- tig r mg "sic ildig lc" H 4, ± 4 4 dtrmi BIBO stl < < Kr m < d mr srt stil sgitig stil III-4

41 BB 3 Sil d Sistm di Dmi III-4 Gmr 3. Drh sgitig stil Schr-Ch. * 4 > H h diffrc dri tw dcs. Sqc 4 H h rm dcs. 8 t Dmii tlh diri sil d sistm di dmi.

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