SISTEM PENGOLAHAN ISYARAT. Kuliah 3 Deret Fourier

Transkripsi

1 TKE 43 SSTEM PENGOLAHAN SYARAT Kulih 3 Dr Fourir dh Susilwi, S.T., M.Eg. Progr Sudi Tkik Elkro Fkuls Tkik d lu Kopur Uivrsis Mrcu Bu Yogykr 9

2 KULAH 3 SSTEM PENGOLAHAN SYARAT DERET FOURER Pd pbhs ii k dijlsk gi dkoposisi siyl jdi kopo-kopo yg lbih sdrh shigg ugkik kudh dl lisis. Sbgi cooh isly sbuh globg kok dp diyk jdi julh bbrp siyl sius yg jdi kopo-kopoy. i dlh cooh dri rprssi Fourir. Uuk sbuh fugsi x yg didfiisik pd irvl [, ], k x dp dirprssik sbgi, x b si 4 Kofisi-kofisi dl prs 4 dp diprolh dg cr yg diurik briku. Mislk rdp sbuh igrl, x d 4 dg dlh bilg bul. S x disubsiusik pd prs 4, k igrl rsbu dp dipch jdi ig suku, 3 isly,, d. d 43

3 Nu hsil igrl suku yg pr ii ry ol, spri diurik di bwh ii. si ] si [si si d Suku yg kdu dlh, d 44 Dg gubh uru pgigrl d pjulh sr gguk idis rigoori A B A B A B Mk prs 44 dp diyk kbli sbgi d Shigg, 3

4 d 45 Niliy dp diuk sbgi briku. [ ] ] si[ si si si d Jik d dlh bilg bul yg brbd, k d dlh bilg bul buk ol o-zro igr d suku sius pd ksprsi rkhir dp dibik. Jik k hrus diguk or lii kr. Nu dg prhik prs 45, k jik, 4 si 8 4 d 46 4

5 i brri bhw ki lh bukik rlsi orhogol orhogoliy rlio, yg scr uu dp diyk sbgi, d δ 47 dg δ disbu dl krockr d puyi propri sbgi briku., jik δ 48, jik Dg cr yg s, k igrl yg kig dlh, 3 b si d 49 Mk ii brri bhw Dg diki, olh kr, k 5 Jik diyk dl prs 4 k 5

6 x d 5 Dg lisis yg sjis dp diprolh, b x si d 53 d llui rlsi orhogol, si si d δ 54 Sdgk kofisi dl kspsi Fourir diprolh dri pry, x d 55 Kr ssugguhy bhw pd dsry dlh rr x, shigg uuk siyl yg puyi rr ol zro- sigl k puyi. Globg Kok Squr Wv Mislk sbuh globg kok yg diyk dg prs briku., jik, s 56, jik, 6

7 Kr fugsi s rupk fugsi gjil, di s- -s, k ii brri dr Fourir uuk s idk dp gikusrk ius kr ius dlh fugsi gp, yiu -. Dg diki k kspsi Fourir uuk globg kok jdi, b s si 57 g bhw globg kok s puyi rr ol shigg. Subsiusi prs 53 k prs 56, igrl dp dipch jdi du, dg uri sbgi briku. ] [ ] [ ] [ ] [ ] [ si si si d d d s b 7

8 Hsil di s k jdi ol jik,,..., k, kr. Jik, 3,..., k, k d hsil di s jdi, 4 b 58 Mk dg diki sbuh globg kok, yiu s, dp dirprssik dl dr Fourir sbgi, s b si 4 si 59 Pd Gbr briku diprlihk buk globg yg dihsilk jik dijulhk,, d siyl sius brri,,. Gbr. Dr Fourir globg kok,, d 8

9 Rigig u osilsi di skir posisi diskoiyuis disbu fo Gibb. Fo ii rjdi kib diskoiyuis rsbu rupk kjdi yg rjdi pd wku sigk shigg buuhk frkusi iggi uuk odlky. Skils Tg Spkr Mislk prs 59 diulis kbli dl vribl frkusi, k diprolh s 4 si[ ] 6 Dg, d dlh priod globg. Pry di s puyi dskripsi grfis yg cukup sdrh. Dg udh dp diplo pliud sig-sig kopo yg brssui dg frkusiy. Prhik Gbr 3 briku. Gbr 3. Rprssi spkrl dri globg kok 9

10 Buk yg digbrk pd Gbr 3 di s disbu spkru. Alisis globg kok yg lh dijlsk di s lh gbil buk pydrh yiu dg pk diskoiyuis globg rlk pd iik origi. Mislk diskoiyuis brd pd d > spri gbr briku. Gbr 4. Globg kok dg diskoiyuis pd d > Trlih bhw globg kok pd Gbr 4 buk rupk siyl gjil d jug buk siyl gp, shigg dl lisis uuk dpk dr Fourir-y hrus gikusrk bik fugsi sius upu ius. Nu prhik bhw s d s d shigg dri prs 6 diprolh, s d 4 si b si [ ] [ φ ] d 6

11 4 D pliud b puyi psg dg fs φ yg didfiisik sbgi, φ d 6 Mk plo pliud pd Gbr 3 dp dibhk plo fs uuk globg kok spri pd Gbr 5. Gbr 5. Spkru fs dri globg kok Prs 6 rupk cooh buk fs dri dr Fourir, yg scr uu diyk, x b si[ φ ] 63 Buk Eksposil Prhik kbli dr Fourir dl buk sdr dg vribl, k prs 4 dp diyk kbli,

12 [ ] [ b x si ] 64 Jik dirpk or Moivr yg yk, j j j j j si Mk suku-suku pgk pd prs 64 k jdi j i j j j j j jb jb j b 65 Shigg prs 64 dp diulis kbli dl buk, j c x 66 Dg * > > c c jb c jb c 67

13 Dg gguk rlsi orhogolis k j j d δ 68 Shigg diprolh c x j d 69 3