L17+Notes+%28Fourier+Transform+-+Examples%2C+Properties%2C+Pairs%29

L17+Notes+%28Fourier+Transform+-+Examples%2C+Properties%2C+Pairs%29

Info icon This preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
Image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: I E “1' ~ . - 211.. x I L 1 ('5‘, ‘ 3" 3 w *5 40$ 21Tw>o vg am 21?“ me I ,2. s‘m 4.x dz, :0 ' (Tfiegrm‘ 0-? am 04A 'CmWC+%ow =03 ; 3. Convolwhou ‘m 'WQ 3; Mw\‘b??\?cm+§0m Mka i J0me damajm Fregéwwcg Jammivk | lofeng-Xo) rioqk) 2 stpfiwfi ZyroPer'h} a—Pw 7rd,: "9‘ i i warm ~‘2muc ‘ (a. 605 .2qu = e 1 +6 1 I y > I 2' KMM‘OTHER NoTEwORTW trams 125mm“ THE. FoomER Tamssoém . % F can) H: m +fl MakuWwaeé‘FQfl = R200) 1 ESL ‘ ‘éfifiéém'a‘ h * ale = FL; ism 9:? cafe.“ 5 , ‘ 0‘6 \ x :2. 5M 1 [IM/Rcd] filo For 'Si‘Mp\e“""“>’eH“6did ‘finCJfioms (sh/Utes), the Baxter TrmnS'CM‘M 1 cam, ‘09. rePresevdzeA as a. ‘3: “(inflation 0er cigars—kc Points Ht “"8 i “ . - V. , _ . 04“er gar ~ ‘ ‘ Espwnev Dammmgr 1 l I “.egm‘inve amlecmAg‘rew—esevcks Mame, ' v Cowmetiovx=dis p lag + and v Qweckwmcfei F3. For now Perkoohc. de‘coms a}; Rpcfifl v the 'F'owvigr TVOLWS'FOY‘M L01“ b8 0., ~€M¢Howmc {refiwepoj “4;:Vk >36dJA’IYTw‘kCV' to a . I ' _ Vagr’cmulax Wm, 10, ‘m amav‘egorwl is re9re5ew6~egl as a, A sum of x ,6" -_ "to Mphax ex Pane/kink (simuSoKdal 'fag-H‘erm?! A;€€grew+ ‘Fr‘exfue res, (L1 V fcnwafiu.) amuxo iwheve lavleflifimcle) Fae) {or waive 4'3 g s C‘ ‘ . » . .. ._ fv‘erwavtcmx; ) the, wekg‘wcm; .- aim/ang ) ‘ 3'27!"an ‘ - . ‘ I ' ' . I FOURIER TRANSFORM PAIRS _ f(x) ‘ F (u) ‘ w“ " Exec. Me‘s 1 ‘.‘ Rectangle fUnction ‘ Sinc function I. ‘ 1 ’0‘": . 'KL' , ‘ ‘ .V" \ ‘ r w ' I ' e_L.« —l 1 ~ \ (J ‘ . R ,W 2_ Rect (x) 2 M 1 V > :: V .1. IX\4 yz ’ - ,, 4/1 1x) wry; (area. mag? a- pé‘mt‘O) o I 7 yz Féwfier TrmnSQrM'. ‘ ,' ,‘Q'n-wx; ‘/, F(_“’3.=f_:” 1‘6 d 4‘” =f;w 1 1T p ‘ , " 7. . ' N ‘ 4m. .- I]. ‘ I V zgfsrucf’rQstin ’ ' " - " ' «h an “I” aka? *~‘%“"f"t.'(//z+x)"f"°° 57¢me +04%? :LWM. ' ; ~ EXaMflg #23 ._...._..._.......... Triangle function [014 Ml-k %. Thus PT» OQ Recruit) == six/1601.3 '2' Racial») ’9é‘ Fact ()0 == Tfiavxfi‘e mehaw é'DeQJg ComVol évrevfow s 821mm? 3' ‘6”!ij COVWOlULJEVOK ‘on?er‘\n}\ Cowolufitow $0‘W?V\) :: Mqu-EQPHCcl/‘lfiow Grazimfiucg ETETHmVxOBXe "mecjhofl . final . . Exponential . ‘ I > _ . ’ 2a ie'am ‘ a2‘+(27‘ru)2 '- I ' Gaussian V ' C3 «(—13 film/ox ' ‘ 5° - x,‘ 'w‘mmx,‘ Fm: fer La? 3; +fe°‘efi (126' ._,,¢ > .F O L __ DY “‘8‘ x 7 XOR.le yoST‘hvé’ n * 1“ L ' n ‘ ll , o (x-jlflw))¢ o0 -= ’+~"2fl* _. lace An A (3 {Dc 1» a3xe .. C‘raz4‘slfrm5x“-/ 0 I“ e —(o<+321m)x /oo. (x 12W) ~50 (a, +11%“? 0 :: I -O éwfio - ‘ ' W jaw ‘ o ' 7 e.ij 2m; w»: -0 " '8 2: “L5,”. :: (wigm) (‘3‘ +31%“) (“H277”) . (94+j21rw)(o¢'j37m7 go" ‘27”) ‘ ‘ 04." ~277‘“ ’ . = 3.311811, vL~Ji2fi~26X+JMLM } 942‘ 'f ‘ 931+(2fl702. r W 5; 07¢; 541+ (2121c); Tka’ "Féwiiél; ‘ $5 Twausfiomgofaal Gem-351mm Us a; ,- G cw $31035 1 ‘ a DO -— ‘lflmx, } 903:] £03) (3 d c126 I (‘3 «co 46b? S7951.» v5 , YJC ' Th6 5” U-KC‘GEOM fibkes 0% v ' ' “they? ate, € flke 4’ 1“ Do _ . « ‘ 0 (Am \ODL 1 ([06 got—260) {6}) ,, 4‘05) Cd; We “we 4th , Listen/x 1’5 CLP‘D‘Y'GA) mm 22. 9mg warm». ' .4, ’ ‘ ‘ La'cfl’m’wx‘lx S 02 SMZm‘XWCL: 5’“ 27”“6" —_> Sm (Ls a,—~—> Do i V '2?“— 0 Wu , ' Taravfore Do wwwf: w w | COS CIXC — g y?afpob grisbfiw) ,L? .4..€.A,:rxV ‘M.'.;~_:L.<_-_ ‘ fl. 7‘ . ‘ __ .1. ... ._<-; l L [gavwgle Q \. Unit step @mfléfi‘ o )C 4. O {X} :2- u m V2. M l X >0 EmMQ‘e 75‘ I _ - k Comb function 'K Covr m 00 E ... \000 I 6 (x nxo) (m -90 ‘ > ~ 0 :21? x. ' _~ i “9 Sande-too « Imam) =fi€W3eJZWAxsaL(GJ 2mg “>436 J. V 53,81 3: C05 217?wa be if:er figs-wag + S '4; [ ,. a (was 15:“ Miami] “1" 15(“fidfi 5765a: “Mist; 51:. _ sin 27rwox é/‘I—s (sewn) +6 (E-f-on +6563 efawxple, «1'1. m £9?“ 7-, . WVs:;:,;fif;”"fif; : ‘ ° Wat‘s“ at, ._ _ CG'LYWSSZ e I, #50):- "R[Q7[w+%) 3: ‘ MM. mmwm “Wm...” M: "wad; ’ ,M'T'm 113$) -gzmaké W 44‘; ham 6 , _ ~. . WK u) 3;. mm , . H, _ 4 WV A. . Cm 211’ 16 {an we) J19 1‘ [242“ (&"wa)4€ iffjflvfifla /, ' , m c (we; rmgm : (w? { awed ,: \ f 604, 247’ (90410») “H‘— + yzf:w¢21%cw+%3cw MA. ,w mu Mwwwwmm ,,_.7..._. m .k * ‘ v m ,, 22‘ ' - ‘ ma _. .. .7 _ “a ( ‘ "' 2—— ,E/ 4-— y 1%) ,. fl , /z_ . 3 + ,. mcwma 7: gab—tag, 'A‘igjfiiiibw" V .w "w 1‘ ' l g r...‘ \ < «QM emvmcm "moo?" THAT THE pm;ng TRANSFORM 093A“: SEQUEMCE 0F EQOAL‘DBTRNT IMPULSE- Funmmns Is:ANioifisé:"12f: $EQUELULE 0F EQUAL ESTANT nMPULsESC h1(t)=1+ ZCOS (Zflfot) h3(t)'=1+ 2K £1 cos (amen 5 ., h5(t)=1+ 2K1: 1 cos .(27rkfot) f0 2fo 3fo 4:0 Sfo f r (c) y ....W.,V..mm._m~____‘(d‘)m Figure 2-10. Graphical development of the Fourier trans- form ofa sequence of equal distant impulse functions. ha): i; (SQ—m (:3) Hap—ii 5< -%) . (2-46) n=~m ) t i i i r fl" 7 ju am, 501;»; 1-5 WsfifloPM/l 1’06 fivsf; ppr . L r a ‘ wage/é 6?) ' 4% 44M ‘ , . ' WV Y‘Ogdr W“ . «A I oomER TRANfiF-ORM ’PQOPERTxE-s we}:ka cam/3' *’ .1. Limaawi‘cé “3mm 01C Immfieg <=> §m0¥ SFeOM ’3’ We?” - _ I . I K gm kx Scale Ckmmfie: COMFveéé‘iw a. $foJ-Td Fume-ho 'i \M/rr? emeds ‘. 5 sPedn-wwt, ‘M @246“;wa '3 (VT), 3. $445M L Translwham __<=—> A, . we” kaSQ' N m ‘LQ (Ce. whim vgflmflrmgmwl M: 1:21: (pagefmlrzkj, shrFA"Wd 4. EDEN} tom 1 3 Rficde. Immge <32? 1 ‘Rofiie sPedtm. \ » Magmhde and ’PMSQ ckmfit§€ LUV“;,gffigfin‘g‘wflmmfifl F(%)gl)¢> {9941) ‘1 561%,? #626,?) M‘Whr ’Derwar‘cw 6; <2) Mex)» ‘Fobgg 42pm. imf‘cecé‘vde (New?) <==> \ow P659 G‘ltflr M Corre‘ai‘fi'm <55 FZu,v)G*(m,|/) (aonjugdey ' (1:? W+mms Hth -—> Power seedmm mm; (a. “pifierm‘hm ‘, ’71 I'm‘\'e?j\rw1rfo \a '. <3. (Lowe tad” To v» n ‘.q’ mnflfi'fiwl‘ga git? We Mb$+ TMF0r+aM7§ \brofaef‘tg’fi a GM. Moaflcgwgwmmhgg; _ Wr- {*gflfjflmgam)“ , - L 4-mmfiogjm9 z fund‘s‘owg (36 Md p re; mes ‘ L * ‘ u I! t y ‘ 1. I? \A (0L. (’de F .one guy/Whom :3 sum? ‘ ‘ _.2/,.‘sow.‘FJggla 3x Egfim «Eweh Fast Jim? othe. ‘ ' 3. mum? Twa’ctowé yoTfi; b3 wfiw‘t’ ’ 3mm" d‘B‘fid‘ 1 I ,_ ' Scum Iaflprodmc'tg ‘, L VH'H'II a . *[gee ac FomP¢W3 “43‘ MINA ow'l’ on Cdedodtfl ‘ . W :- ’ o; Mahm Es (new "9‘. Keel.” mutt Mme . _ » " ' fiwxc’fiom (he Commhivx‘gor sham} newwcflcto“ and Boxéfid o r ‘ M WOW Cwflgehs "mama "my macaw ~. 1“D Convdwflpfl: one,“ rfikflgfiL 1" $0M @Nowm Qw’c‘xbm in )4 0am; a? l ¥umolciofig ‘vgrkoces another fimcfiion ‘vxvézdov \“txz‘gh ‘ C49, “vomifigfl ‘ .1“ HM)“ figme’ AW‘SW‘OJ‘V‘ ' QVDEVMOSI etc) I “*3; Z: Convawftam. ,‘T‘M um.“ n21?" X~“v=‘~‘-"’i, .mr .1 ;; 7 ~ ' V V. f“(%% “Fats Magi) a 5:“: éé’WGfififi .1315w ,. , w n ‘ he .graglmoi' 9% émvs. aafigrzu ‘ _. ; , . _' . wmmm . fwd“. _A._,. _. > ,W . ‘ T, ‘. ,, mg. m...._,.‘ m.» ‘ l ,“i’ W“ ‘ m. firm, ‘QWM mpg. ma “IAM‘EMM 3-, w. ,figgdrggm “t. 5 Ha. “Mm? nihéeflg fimww Km 6% magn-fiwéfiwlfiw_ " ‘ . ‘ 7- L I ' m5} " a fiOFarfiw 3%!” W‘fi’ad M753 ‘75 am A. u ,_ CMWWTMM Méfi’r, Me,ap‘r‘fML'-Ff‘¢e?f7§3.y ., (@335? fingfiégf’w) %[ . Ext), 0Wvi;gwfiéflzmaEWlé @KL ggnvokiuhaw fizsemm {fiwmafimér rfiwzv‘sfimfiikerMammalLN m , a“? Ma wndflfavbfig, .. 7, m M W M ,; . 3 ,f‘::‘:c‘,_finfla.‘ud,,,‘tan 444:. ms mumgveéflflmwmis A w Q‘xfimaé b ' A. linear”, rpmfia’vfi‘m WM ww’ahaam‘b' ,, ¥_ :EMa-yyagség’oefijm, - .A A, , ‘ s 7 #r Tmsvw "a mflayfic “h: amfi _ thwlxéjMfi “bk H; Spacdfimwmfimgfie gawk Dam. 0.2%., ‘ ' j_9§..c.oma\w+‘mn mime. 59am. Am M, 1‘» a wimlmit‘am _. . WMch p\‘xc.gu‘mnfmiw,?‘m rueng-,'* D4,,ma1nimg » MawY;I.i_¢wmi2¢m,,.‘m, flenfiem.“ um _ .i$.£%§§w_a«i%flg 5* QQRWD lw’c‘zmyfsm'hm Frecg,u.wcg.'bmmnm i i 7 € 4 \ a “FOUR‘IER TRANfiF‘ORM WOPERTIES “5:39” If 1. Limawrfia ’. 3mm cg Imaeg (=3) ém-o-G spedmg 7/ ( fl’v G Scale Ckmcge: Compressing a. ‘bfojfia‘ Fwd-r0 7 'I k emeds “. 5' 9P9.cher tw-Wectweaw‘é {VT} 3. ShKQ-lz-rw ‘. Translm-kxovx' <”—=‘> .- 1 MoaS‘Q’Ngg MA. ‘ ' Li. (“Cd'ltt-wu: “cat/WE-su‘l": [wt/62' I; lgi’fi“ 1?sz 1:32 “8?;4r315j ski—FA re: rm 4. Ro+m+t0fl ‘- ko‘kcde. Immge {=9 Rain-he wedrm \ Mmgm‘rkudfl mfld w"+2-¥zoi}¢%§+ly%\xh(wsih84rm 5. StaMME‘Hj’I . F(*)g)<e‘-'> ffiufu) \I 567%,? 156—26,?) flaw fwfu mm (a. DmCW-hm 1 ’Derww‘cxvg ¢=> WP Imus ~Ql‘rer- Pass filter Covr‘th’MW <§> F(“IV)'G*W (Maw/+65 (IL-F Wwmes Maud —> Pcwer seedrwm ‘7‘ Tw+€ aka/H0 \A. ‘. :wkecéyvalve, (News?) <‘—"—> \ou.) <5. Covrekdm‘o w '. $7. %“Wfi@flfl“33 ‘tke, mos-l" :MEFOVJVa/wfi “Fro‘bev‘bglg % Grmgkicaflég IlleJcrofceci ‘Cor ‘Ewc 1H) Red Pat/hag; : Am 2 7H? ifjfa )ach—(x) o’x ' ' kn Convomjou 01C 2 (Martens (3C Md g3 reg cores 1- EMA ’gb )L .2. ssz ‘ '3. MLLHWP xumafiowe \Dotld' \a gawk 4. SLAAM tapromct$ r a 7 I [I‘ll] a *[5ee aCCOMPCLVLEKM MWAmd I on Covwolwhfi @ CONVOLUTIQLS :2 "One. (wwohow ls he,ch "91x83" whlg the other hmc‘fiom (We Comowivfior SHAW} human lfi'ghflnedflavui Bag-36ml, 0 r1 1—D Convontiom : one. Vanctmw (menale is 3-, ‘go‘A Comrva QLWCHOVL 1W )4 and lat ' ’(Hif \each .,‘ .A, .., H “.9 «MW \ ’c ' 2. sh“ :- ‘ E3. mudfitfhs "’ CWOWOWV‘O“ 5% '2 ‘P‘W‘C’VOM 7(7mcm‘383 another Eumfiton may or Mm?) 'ka the 30mm AomoJM (.63. ' Qflemwycfi) cone Cwmc’fiowRé "sweF‘t - Past" the ofihe ' - Smkav dgihfre ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern