Mol 9. Prtmn 9 s/ 6 INTEGRAL OURIER 73 9. DEINISI INTEGRAL OURIER Mr t mngsmsn ons yng brt :. lm ons stbl Drhlt t-t ntrvl trbts -LL.. M Torm Intgrl orr : onvrgn j ntgrs bsolt lm -LL. { A os B } sn A mn B os sn Dngn mlht hsl j lh st tt snmbngn. J lh st tt snmbngn t hrs mnggntn ngn srt ss Drt orr. Jngn tt bhw t ts ons-ons lh tt rl. Prsmn n ngn brssn hsl nt Drt orr lh nyt. Ss tngn nn ng-ng sbt st Prlsn Intgrl orr. Torm Intgrl orr J ngs ontn sotong m sotong st ntrvl brhngg mml rvt r mn rvt nn str tt n ntgrl b b lm lm m t rrsntsn olh ntgrl orr.
74 { A os B sn } A mn B os sn D tt mn t ontn nl ntrvl sm ngn rt-rt r lmt r n lmt nn tt trsbt. Contoh : Cr rrsnts ntgrl orr r ngs j j < > Pnylsn : A os os os os [ ] os os [ sn ] sn sn [ sn sn] sn A. B. sn sn sn sn [ ] sn os os os [ os os ] B. { A os B } sn sn os sn sn [ ] sn os
75 Lthn Sol : Crlh rrsnts ntgrl orr ngs - j < j j > Kn Jwbny : os sn INTEGRAL COSINUS DAN INTEGRAL SINUS OURIER J ngs gn m ntgrn os mrn ngs gn lm n sn ngs gnjl lm. Dngn mn : B sn os os { A os B } A sn { A os } A os yng mrn Intgrl Cosns orr. J ngs gnjl m ntgrn os mrn ngs gnjl lm n sn ngs gn lm. Dngn mn :
76 A os sn sn B { A os B } sn { B } sn B sn yng mrn Intgrl Sns orr. Contoh : Cr Intgrl Cosns n Intgrl Sns orr r > > Pnylsn : A os os os A lm { } os lm os sn A lm os sn os A. B sn sn sn sn B lm sn lm os { sn }
77 os sn os sn lm B B. M Intgrl Cosns orr : A os os os. M Intgrl Sns orr : B sn sn sn. Sol Lthn :. Crlh rrsnts Intgrl Cosns orr ngs > < < j j Kn Jwbn : os sn. Crlh rrsnts Intgrl Sns orr ngs > < < j j
78 Kn Jwbn : os sn sn ORMAT PADANAN DARI TOREMA INTEGRAL OURIER Torm Intgrl orr t jg tls lm bnt : os 3 4 mn j t ontn sblh r hrs gnt ngn. Ths rslts n b sml somwht s thr n o or n vn nton n w hv : os os s vn 5 sn sn s o 6
79 9. DEINISI TRANSORMASI OURIER Dns ngs sbt trnsorms orr r ngs tls bl r 4 n rolh brt n : { }. 7 Sngn ngs n tls sbt trnsorms orr nvrs r ngs bl { }. 8 Contoh : Crlh trnsorms orr r ngs bl bl < > mn onstnt ost. Gmbrlh gr r { } trsbt. n
8 - Sols 4 sn sn 4 sn 4 J. sn bl bl
8 Sol - sol. Crlh trnsorms orr r ngs mn onstnt ost. bl bl < >. Crlh trnsorms orr r ngs bl bl < >. TRANSORMASI COSINUS OURIER Bl ngs gn btn bhw : n { } os { } os.
8 Sols os os 4 os sn os ] sn [os mngngt bhw os lh ngs gn n sn lh ngs gnjl ny trh vrbl. b os os 4 os sn os ] sn [os mngngt lh ngs gn yt nt t mn lh Trnsorms osns orr orr Cosn Trnsorm
83 TRANSORMASI SINUS OURIER Dns tls ngs sbt trnsorms sns orr r ngs n s { } s s bl s sn. ngs Sngn ngs n tls s sbt trnsorms sns orr nvrs r bl { } s s s sn mngngt lh ngs gnjl yt s s nt t mn lh Trnsorms Sns orr orr Sn Trnsorm s
84 Contoh-ontoh. Crlh trnsorms sns orr r ngs > < <. bl bl Sols os os os os os sn sn sn S S. Crlh trnsorms osns orr r ngs. Sols sn os sn os sn os os os os lm lm lm
85 J Sol - sol. Crlh trnsorms osns orr r ngs bl bl < < >.. Crlh trnsorms sns orr r ngs-ngs : - b -. 9. 3 SIAT-SIAT TRANSORMASI OURIER Dlm hl n gnn nots nt mnnjn sngn trnsorms { }
86 { } St-st Elmntr. Lnrts Bl n m onstnt.. Tm-shtng Bl m. 3. rqny-shtng Bl m.
87 4. Slng Bl n t sm ngn nol brl m nt onstnt yng brnl nyt rl. 5. Tm-rvrsl Bl m. 6. Smtr Bl m.
88 Contoh-ontoh. Btn st lnrts ts. Sols ] [ ] [ ] [ ] [ mn ostnt.. Btn st rqny-shtng ts. Sols. ] [ ] [ Sol 3. Btn st-st tm-shtng slng tm-rvrsl n smtr ts.