formula_sheet - 3.4‘ I Proxy-47f: {algé‘Q—iddx :...

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Unformatted text preview: 3.4‘ I Proxy-47f: {algé‘Q—iddx : (x6) . V egg": Cosxztjs.‘+v‘)§ The W form of the Fom‘icr series f (t) .= a0 4- Elan coé(nmot) +b,l sin(}ch;,t)], where To is thé‘pggied of f(i), (Def; n=l - 0 - 1 ta+To ‘ I ,2 tan}, ' ' ' 2 ta+To V , an =— jf(t)dt, an =— jf(t)cos(nco,t)dz, 1),; =— jf(t)sin(nmat)dt, n =1,2,3,... ‘ To to ' 1:) to . ' I; :0 ' ' . _ m I . 1 [-0 +10 I . ; I .Ihcgmngmjglhnnfa) = ZDne’m’“ , D" = T— ! f(t)e»""°"’dt, -n =0,i1,i2,... . "=4 a to szJ= fzftae’Jwtolt- . {/ékzfirfwP/wJeJ, 01w —a’ . ‘0) m to+7b Pmm’mwmmformtpcwfim ' fa): P, = Z ID,'..I2 =1; I f2(t)dt 0 to parsevarsEncrgymomformalmcuonfa): 5531; flF(cb)|2dm= If2(t)dt ‘ fit) as %fé—> 21[;/u-%)+,qw4%) X -—‘x_ '_ _, iii-7‘}: 1> COQXZ‘ZLEJ 4-218“, ) S/nflije ~2J€J 51$(xiy)=5m;‘“5)’$ (ax-Why COS x cosy > 1 [toys (>073 + “Sod”? Cos (Xiy) :Cofxaagy7S/hk5/‘r‘y . , .- ' - - - L ' - — Cos(x+ J _ ,{osz’x : (/+ (052)!) $4th $1.579 2-[0956 ‘1) _ ’ ‘ smz x =55 (I- ca;sz (an Ila/#57031 3 ~w ' ~ H Smcht): SID—X. 1“ ‘11“ _. V ‘ ‘ .. Side {ma 3 @1wa ' (Kraut/b 54mm} Cascade, D‘AL. z - _ Iv”- . 7 ' me) QIQACHL‘J {'A'Q hian 5'2]an value. . . n ,. ,. . ' I - - - 7’; 2m r] : power efficiency 1: I, + P; m, x/oo Z , c m ~ Indefinite lntégrals' I _ ' :0) 6(0) fudv=uu—fvdu . I I 1 ram 1 no I - a+ju , . ‘ ' ‘ a ‘ l f. f f<x)é(x)dx=f(x)g<x)—f f(x)g(x)dx ~ . 2 ‘ "H’ 7 a-ju 0° x." ‘4‘ . , l - I. 1 . 3 {m a‘+u‘ “>0 ~fsmaxdx=—-cosax cosaxdx=-smax - 1 . . In a 4 I u"'um (c +1.”); I . a > 0 . X . 2a: ' ' 24; I . g I fanzaxdx=-2-—£1:I— 5 ream") (¢+;~)In+| “>0 . 6. ‘~ 60) 1, fxsinaxdx=-13(sinax—axcosaz) . ' . a 7 I ‘ 2:516) . , ,1 ' ' I I . - ' S . c’“ ' I haw-mo) fxcosazdx=—z(cosax+arsinax) ' - ‘ ' . ‘ {1 . . 9 ‘ cam x[l(o-m)+l(m+-wo)l I fzzsmaxd;= Faaxsmax-i-ZcosaxI—azficosax) I - In line»! I I jn[8(u+u.)-J(u-mo)l l ' _ ' , 1! Id!) ' xi(u)+Tl— fxzcosaxdx=—3-(2axcosaz -_2:inqx+azxzsinax) ' . 2 J” II . a _ r v . ‘ 12 apt j—m _ . . sin(a—b)x sin(a+b)x ' , ‘ ' ‘ I ‘ mumbxdz=——————_— 1 E u- - J” ‘ / 2(a—b) , 2(a +1») “ 9”: ‘3 '°"“""“"" 2‘“. “’+“"’+°’°”C'EF‘ . I I _ I I. l - _ u no fmambxdx=_[cos(a b)x+cos(a+b)z a: #1’2. I4 mow-(r) zjmu a.) u “mung”; I 7 . I 2(a—b) 2(a+b) r u .«ang ' .__“°_ a>0 3 ' — ' - - (a+jw)1+a§ fmumbxdx M a: “I ' n+ju ' » I I I 2(a+b) . [6 I t casual“) —Wj~)l+ a>0 I I , l - ' t . a" - ' ‘ fefldx= :2” ' . I I I. I7 . "m: - _ . a I ~ I fxfid;=£(u41) - ' . ' is ' 7mm" ‘ “(27) . - ‘ I w I a: . . . _ . .Ae) £65661). 1 c. *4 f. ‘ xzf‘dx-eu ’1 Zax -' i I ' 20 Wine W' ‘” ‘7— ; ‘ ‘Ts‘a’ ‘ +2" ' _ I . E (T) A(W) . _ an - g . . . e" ' 21 ' I —-n 5 -n ‘ =— I ff‘nnbsz:a2+b2(asinbx—bcasbx) . n;- (l n mo";- (m a”) ‘ H m T I ' 7 .4: ' . . - , ' I 22 NW 4 an—xww _ ff‘cosbxdx=a2+b1(acbslix+bsinbx) ‘ l d‘ l _l x I ' . ' x2+a1 x = :tan 2- I FourierTransfonn Operations - ' " 2" dx=11n(x1+41) - 1 +31 2 ' ’ Addition ‘ slmflam . was» 0:0») ' ' . gmfipuwm , I 236;) :3?) )II . I . : :- . sun“: I I flat) I ‘ I flaw-E) F V Tune xhifi - _ . - M FM Wm 23.122 29:" I , . Tune convolution _ m a”) _ t _ n“) ' a“) amaze») (PF [‘9 3/4 C0 SDUC 'L‘ + Ff I mbtk‘d] * I Wmmm‘ . game). _ ~ ' fimmtozw) M I _w I _ Tune mummy“ _ 3} WWW cbmbe'L‘A coclwae +‘kp mm] ' . . .T".W°“ ' A” ' FM] on m baQQLaJcM'HeFZMQ-HIB) :Izgqgmi wlIIwre "5: my; analytimynlz. ’ fifimfi/Mmltfl (Asa/56 ‘ I t; ‘ ‘ _ II mucoswgtlmhltM/hw‘z‘ . * Wfihc uaJUfiL ‘95Un-EJMJ Scumfluj (Fermi Ts I ed; o<I=¥wII {-6 btgero- ...
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formula_sheet - 3.4‘ I Proxy-47f: {algé‘Q—iddx :...

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