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Prévia do material em texto
Transformadas de Fourier f(t) F (w) = F [f(t)] a1f1(t) + a2f2(t) a1F1(w) + a2F2(w) f(at) 1|a|F ( w a ) f(−t) F (−w) f(t− t0) F (w)e−wt0i f(t)ew0ti F (w − w0) f(t)cos(w0t) 1 2F (w − w0) + 12F (w + w0) f(t)sen(w0t) 1 2iF (w − w0)− 12iF (w + w0) F (t) 2pif(−w) f ′(t) iwF (w) f (n)(t) (iw)nF (w)∫ t −∞ f(x)dx 1 iwF (w) + piF (0)δ(w) −itf(t) F ′(w) (−it)nf(t) F (n)(w) f1(t) ∗ f2(t) F1(w)F2(w) f1(t)f2(t) 1 2piF1(w) ∗ F2(w) e−atu(t) 1a+wi e−a|t| 2a a2+w2 pa(t) 2a sen(wa2 ) wa sen(at) pit p2a(w) f(t) F (w) = F [f(t)] te−atu(t) 1 (a+wi)2 δ(t) 1 δ(t− t0) e−wt0i δ′(t) wi δ(n)(t) (wi)n u(t) piδ(w) + 1wi u(t− t0) piδ(w) + 1wie−wt0i 1 2piδ(w) t 2piiδ′(w) tn 2piinδ(n)(w) ew0ti 2piδ(w − w0) cos(w0t) pi[δ(w − w0) + δ(w + w0)] sen(w0t) −ipi[δ(w − w0)− δ(w + w0)] sen(w0t)u(t) w0 w20−w2 + pi2i [δ(w − w0)− δ(w + w0)] cos(w0t)u(t) wi w20−w2 + pi2 [δ(w − w0) + δ(w + w0)] tu(t) ipiδ′(w)− 1 w2 1 t pii− 2piiu(w) 1 tn (−wi)n−1 (n−1)! [pii− 2piiu(w)] sgn(t) 2wi Lembre-se que: 1. F (w) = F [f(t)] = ∫ ∞ −∞ f(t)e−wtidt 2. f(t) = F−1[F (w)] = 1 2pi ∫ ∞ −∞ F (w)ewtidw 3. f1(t) ∗ f2(t) = ∫ ∞ −∞ f1(x)f2(t− x)dx 4. pa(t) = { 1, |t| < a2 0, |t| > a2 5. u(t) = { 1, t > 0 0, t < 0 6. sgn(t) = { 1, t > 0 −1, t < 0
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