0% found this document useful (0 votes)
36 views34 pages

Fourier Transforms

math

Uploaded by

dhruvikadivya
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF or read online on Scribd
0% found this document useful (0 votes)
36 views34 pages

Fourier Transforms

math

Uploaded by

dhruvikadivya
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF or read online on Scribd
You are on page 1/ 34
“—< TaFinite Fevers Patino | » 20 eft 7 eNt ® b nes 9) if bo de 2 (Jems (#(u) - 4 Ca) 7 vohane Fle $4(x) & 1 ; oo ) (ama - a (Gide dx 400) ($0 Reve) * oO deve glx) (ola 58 odd) | xe | 4? ( ‘= CoRluda = } a (acon + Leming oI SS Hy 6 EZ Catering sb Sn bas) cht be ne 2" co tarot, + bob) ott bt nt 5) | 2 Sint da = a (a Snva me ptorbx) : arto (ueg|(wien] -(u' Vv. ) i UO NiO da = ob oly nenied esith +(u"](vsloa ce: ave daorree whne u's Se us dul du | uy (vn ie Pure Va a Fotmyulae ——o 1, Founies Transtor(e7) Cenparte foreiers Rrsonapens, FL oof 2 ECO) = me ("ee E2% ig nv -v 9, Enveese counes Taenk }eorn (se7) 4 nee who | Phew): fae ge j Ett) Oo det “7 | 3. FOUBMLT _CoRINg Teank}vara (€e7) and WR Tavtere Ae . Bef dears reted= (E ("re CoReen ln cheats das & Feces Cogoln dok i 2 48 4 iER Toverke be EAGMRE FST Lond ith lover Fgh tte) | cz €s lol) = a a Lea) SN kK AX ° Pq Ce) Sinan. ct So ees: fas note } if Eade te} tren £ (dX) 2 €e td) and Th aCeade~ Fld tran Fla) 1 Fstet) Paroles LOL TL WO a. h> eine the Fourier Trectfam of Fears i Com est : ethemoige We ee = Ay S ° Con . a a F(x) eS Vea € ak dat =} a " T4e yen dm ~v mL 3 a . : a tg § CoRnt em ay | = ; (i Cok + Sin nh & ol Gate o tt >? Bis ~ Cleon + Serf =. Geeane AD -f - dda) _ in | < t= Lt t- 2 Bs a (x) Coke ax = “BU E D Gf rs Coan dn | ee x) Conocne sal i J ah ' ole u v u “ =S( J (too ( #241) - wn Ee)! +(e» (284) - enc eet § | = (2 4( (25s + Se)-( (0+ &t2)] | “1G ~ Ses) - (2g so)T Gf os sae pea eta) Gf Bot t= ream 1 L#O . bok OLNLG 3) Find © S87 ons f 5 aro a j : ° ottawte ~ : eo to a aa | oR x 8 ref Jef i Penson = Gi + ff 4x) Sinn, dx , o 4 ° a 4 ( CoR% IN LK ie ae ie; (Se Geri) nt Sonlete a}dh a , Fee i dF 9% aot Q { = CORED scala (* a Je x1 a J, lok] f toto 4 Loko I ett ant o- ef (torsade St 1f Att Hi a CoRK+I)A -! + tor 16 -! pest oe} A, etd) =~ ef is 20 tt ,o} a \ah £0 ° jal? flo. inlfo my 02 44, WoL > KE -arK DH FE, KHL-AL HOG] os v ef e li, -w ° ae oO cad Ldouts om jem oe oa aes aff’ (af "aceon " =o Pa ~a = 2 pike - = we LF 4 iu uv ia (a, s)-(an(£ sy) ir = ge OD (2 a} (ects Pela galt 9 Le | W ot a ge a S 4 Atay Fee et 4 oe 78 2 oO oxo 3% { = (: iT oN QQ 2g (Aue, 9 (ee ! TR PP ale | f ¢ te | sehsinant Ha CokAk _ y gmac a oS t 2 -2,f Cale Brae + LA CoRAeL - atmaat N90) 3] ¥)- Fe) sf (e229) Grol + Ax toracc | #0 alle: in ainve grOdem fale Flo), fo AR bev Fo (XIE EG) pow twiefnttt, (xl ay fds craw Int La O otnemorse fo Al -0 ° a a a Tre 0 ° (- % (14+ 4) 3 ged Wa KO he x40 ~ PKK K-O gts) : 1-4 “OLN LO 14% wLKLG Oo Ff aca ae at Pm) 2% ‘dtc el q (4 ( (+ \ (Hes \ > ye ey aT Ceaes "sn as Soespen a al 0-4) (24)- cae ) (c+) HE) CICS)T J a © oO . - 2 Zit® sik “am 4 (¢- ia | [aaz- ee] ex exe . a ° +a — + a] [ee te a+ on ae xo Phe s ai fo oD a 12 42e ~ Sfa5i Kx aah Pot ace ae + yee t “aut “ ao* c= i. RQ. 2 dX eae ax™ & Qi a a gtd at z On oa -~ 2 _ uy Sad | @ Cokaod SR [oe ee axe a rene y a age | Conant 1 2a Smal xe a emd FT 4 #0 ° _ a ea 1 40 a x a 4 Cx) + HOOK x70 He 0 mf 0 rol d a Cu) & due aK «| CER 4 Qi “we 8 a . a ° an oh ane Be ee an | 20 i ° -w | : os rm ~ Ca-iek)% eo Ge 72 dm + aa | Fey a Gy 4 , ( farin)a 1 9? te a ee ‘enor T, arid Grid) so = (Oi) K Jo ZT a Ste ie) ~ ay ee eae) Lam Ct fol) H Stn 8 Petre, tern (fbn) Fr URE L!tagbhroty ye - lw & Cot toe) H Ap—99 0 denis Fe Rech: Seca a dat 5 Crowe XK 9 Gondtank wtb: wege crt Seta ea fie ea | {Peres 1 ol ESE eal ellen sal) a-Ve q fox) = art en a “fe Cz = sort ae acl & “~ a EL poblery wohith rene) shat = & & Y Find Fours Prerareen fea 2 gO aro, Henle Rhos thot 7% ig auf REPL wate F 4, . Wye ben 2 ef dees ee [gh OT dn. be edd | Wd Ry fol gi, @ loryided - ot aBetoln t= Sowa ion} {font 2@m(3g) + (Cay (sa Hor ace | |; . adus dr = on > dE no Chon ian Leg . ae a Hh tt he Me} ” a BS ("e oO a) aha a a i 8 (at ig ewen) Pp - AL; e, fe oe “i ay © "x * fin A c i at - -(%) — a Q c Show thor ava ik Rend RO pW Gad VTE Fours Cwo&nR Crom fom. \ ‘Grr the abe result with OF GE aed Sate - te > {eay: oO, eh 2 fay, we have 9, Le gahe why ZS Shaves Pind Arg Po} Hater Find TET of Feeds €% ahaa 2 gone Ehets E- ve rs hol. | : ° © atk ; "8% te e dt of ory e Autens—fotaiantef ch aul) ao haty a«(32)4(i0)- (xy AG BEN] © oe = (er LAY, oF 2 ; Rerik Pa a) eh 3% eit A “8 rx 3 ve cae LX) Sex) ae | eae a -v gut xtihe b 2) dacdr ft) atot€ \ te (5H wr ef even & ° Se at a @ % one. (3 xe -%, ia e a9 \ er dt = Se | 27 § ; € —=— 4 > g aot at i 2 me @ Reven Ete sete . P Find Foures tre mfeom of dtm = NM aM. "a Lakai 2 Fla) s mS 3% en nie fa ee WY ahaa eS Ban tents Fit} “1@ PCE CE* Cat ayy -f(e-3 oy 4% Show thar eS 9 BYE WPCA Wirt. 87 be tet fen) = x ew Feats =m ek. eM tte) fr) 12 ode , Qo aay Ti Fei xe if-o font eke OM oe ERO vem @ in % aa 3% 2 reahne” J a6 a eghn et Gia é a Solve the lotearsenk Rapratin ot find fox) fro the given Aaycortiin , ° 4 J fo toreendn sé ° eae (qe) 5 ak Frazee | edie ga Tech Feld) . fm)= Fe ‘hee Ge f= fe Be ee . wo ° 2 ! EX CoAnn do 5 2 Ne’ a | = Nera e206 w+ BL 0- S Ceworyare)} F0)* Sharh] pete OF X41 7 t-& 1y ) PO ornaty dx ° Co wm Sho Wwe toh 4ea)4: & \ pee Gina dx t Eq (a) « (: to OLX jt ° x>I ° IN r Kx ae) PRE x“) eek) “x>) oO rest firey fo | fends es" fese a= 2 | Fs Co) Sx dol 7G ( (f (ine) San dK 2B f m0 ge) en a) To e@e)-E a an 37 be To fwd foo bed tS ew: {Oo : C 3 ( F(x) Iman dx ' ce STi BR Grol tol +f2@ Mn ey axl : fl ga : a OC alt it ea tenelnr XE? . "Re pe TA sails 4 } £-%§ fees ta0) «9 ( sefse seer) | 75 | Cott ea ein = 143. C018 - 20 | @ au . DCRAX - WKI—' fads - 34 sone xO 2 - « of KI he { Pen) Cote en = 7" 2 a7) Henle deduce - * sinf « f te tote aa. Fo SBE 2 Te ° “er > Yo wir Fehttn he pi ~ $ cm) CR XX dy | « (2 te x oc x4] : GJ n of ee) | Fefsoage Felt) = Is ber eS Tawe FCT 4 @ 5 fads cctbewh= pi oe ba * "6 Creot) Coden dol 2 oe a) tonetn dof FE | % = 7 (1 2) ( sn) - cote. . Seductiny! ving ® no ” § F (ELEE) Conan dx he ead ° o>! f (ee tog - (op toner dns SL) I ae 2 o x >) Por 420 } Cogonel t, (2222) tegen des BC) ay se C0888. suf 2) Sn AP. 58 H) 0 =) 5 asn"(%) daz a > ne 2 @ur wet =) daz ede 2% = Fr < Agirk = 4 . fdr = Se BO = ree 2 D ) ( dt aE. ZL. Qrorkany wohith aunts Tradbomu meee Tron fon lefty ' txleg » etnd #54 teers J #20 8 tal > a Hente eMoterote oO [sma tone yy (yy J Smee ay 6 4 "a : 0 . redse tions of ("4 (af | 0 Fd | es a tol a. Polya Jax sia | e Fa : (2 aes a, _ \ els 2 oe me, At no) e (4) ” (8a z( Ti (8) evtotuate f ine -7 uke AT 2 - Snack) aigs% fd: € ‘Seong | te am - = 4 ( Saas (Cosxn Tomax x) dol 7 -~W 30 oO “ag feat em ax} ee dL ft) = Af L eeu ies dct 2) £ ad GhK dee 2 Doheny Tf (W % Tse CoRetne dizg y lala oe of ° zl > To hove the Reyrned MntGyoaul | inteachenge KAY, vO 7 ( Sam CoR LH dy = \O Jal ea {| Satter —o on 0 tal >a W7 G) Te enolate SVtsnd Mikarat Pub x20 Io © we lense 0 € (4,0) a Find 6 i fms ie a ° \Rl> a | deduce C) Seen 2 0) ans 3 oy Setar Cok LY) da ° xs “ a I e t l re rome heehee ofa” a 2.42) el%* a ( Gydea®) el ae mice * a ae) (om ( * “() ( s)eo(SS) id@ fla a os 228 AST all tx? J Re’, ” n a { - gxt 4 giao 3a ( Sat oe at - [2 eee, stag) pga ) f = (2 a _ 7 & i We an al Re : a j - La bea sina a x eye 2 SLO = Oot CORA ) a een beeen LED | Dedv c+ 3 fog Tate TET F Co), vo) t@)e 2 (ecu 2% dot [2% ne . 20 dads oh a Strela = Ate q\\ .» fe ae Gi (ee) er Poe 2 £ (Sido Ox CoRH0) (oer -} Snel) ak cn x

You might also like