EE314Tables

EE314Tables - TABLE 3.1 Short Table of Fourier Transforms...

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Unformatted text preview: TABLE 3.1 Short Table of Fourier Transforms GU) 3(1) I l e"mu(t) a +j2nf a > 0 l 2 eatu(fr) a _j2nf a > 0 2a 3 €_a|ri W a > 0 4 te_‘“u(t) a > 0 (a +12nilrf) 5 {Heiafu(t) a > 0 6 6(1) 1 7 l 5(f) 8 ejzflfu‘ 5(f —f0) 1 9 cos anot 0.5 [3(f +f0) + 6(f —f0)] 10 sin 2Kf0t 10.5[51-f +11%) — «5(f -f0)] _‘ 11 um éaiijz—HJ; 12 sgnt ,—- 2 J; Hf j21rf 13 cos 23rf0tu(t) 3[5(f —f0) +5(f +f0)] -i- W 14 sin 21rf01u(1) 4%[5(f —f0) — 5(f +foll + 2 15 e—ar Sin 2nf01‘u0) “(a fling: {WW (1 > 0 0 .2 __ 16 e—arcos 27rfot 110‘) W a > 0 0 17 mg) rsinc (Eff) l8 QB sine (2m?!) ' 1'1 19 A (i) isms? 5?) 20 Bsinc2 (1:13;) A 1 21 Zfifio 50 — nT) f0 Zfiwe 5(f — nf0) f0 3 5.: 22 H1202 eme—2<mf)2 TABLE 3.2 Properties of Fourier Transform Operations Operation 3(1) GU) Superposition 5'10) + 820‘) G1 (f) + G2 (f) Scalar multiplication kg (1) kG(f) Duality G0) 8 (—f) — - L J: Time scaling 8 (at) [al G (a) Time shifting g(t —_ro) G(f)e‘j2"f‘D Frequency shifting g(I)e}2”f°’ GU "f0) Time convolution g1 (t) * 5120‘) G1(f)G2 (f) Frequency convolution g1(t)g2(1) 61 (f l * 02 (f) '1 Time differentiation ddfifi‘) ( jzirf)"G( f) . . . r G(f) 1 Time integration ffiw g (x) dx + j G(O)6(f) 1 ' E.6 Trigonometric Identities 6053 x : EB 005x + cos 3x) ijx 3 e :Cosxijsmx sin x=3(3sinxasin3x) 608x: %(er+e—jx) Sin (xiy)=sinxcosy:!:cosxsiny I A I cos (x :l: y) = (:0st03}: q: sinxsiny sinx z —_(€’X * 97’“) tanx :i: tany 2} tan(xfl:y) : H . l—thanxtany c05(x:|:5)=:FSlnx ' 2T sinxsiny = E[cos (x ——y) — cos (x +y)] Sin (xi : icosx l . cosxcos : _ , 25inxcosx= 51n2x y 2[COS (1 J’) +COS (X+y)] sinzx + c0521 2 1 . 1 . ' . smxcosy : §[sm (x — y) + sin (I +y)] 2 2 COS xisin x=c082x acosx+bsinx = Ccos(x+9) in which C : \fa2 +52 and 6 = tan"( 2 l . cos x 2 EU + COS sin2x = - COS 2X) E.7 Indefinite Integrals fudv=uv—fvdu ffmg'oc) dx =f(x)g(x) a ffoogocwx . 1 [Slnaxdxz ——cosax a l . [cosmdx = —51nax a ' 2 ' ' 2 f‘sinzaxdx = g k sulfa? fcoszaxdx : g + Slzaax 1 fxsinaxdx: 7(sinax—axcosax) a 1 . fxcosaxdx: ——2(cosax+axsmax) a 1 fxzsinaxdx = 7(2axsinax+2003ax—a2x2cosax) a 1 . fxzcosaxdx = —§(2axcosax * 23inax+a2xzsin ax) a . . sin (a —b)x sin (a +b)x . _ sm ((1 —b)x 5111 (a +‘b)x 2 2 f cosaxcos bxdx: b M 5 dx = ——— —— fi 2 — fsmaxsm x 2(aib) 2(a+b) a #19 I (a b) 2(a+b) _ cos (a —b)x c0s(a+b)x 2 2 femdx: we” 3 b dx=— _ ‘ b fmaxcos x [ 201—16) + 2(a+b) a # a ax em xe dx: Efmx— 1) 2m 3m 22 xe dx=—3(ax ~2ax+2) a (1X ax . _ . f2 smbxdx— a2+b2(asmbx—bcosbx) e“ . femcosbxdx: 02+bz(acosbx+bsmbx} 1 l x dx=—ta _l— fxz-l-a2 a n a x l 2 2 fxz+a2dx=§ln(x (1275522 ...
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EE314Tables - TABLE 3.1 Short Table of Fourier Transforms...

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