Signalbehandling Formelsamling
Signalbehandling Formelsamling
Signalbehandling Formelsamling
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B.2 Fouriertransform för tidskontinuerlig signalΩ=2πF1. w(t) =F −1 {W (F )} = ←→ W (F )=F{w(t)} =∫ ∞−∞ W (F ∫ )ej2πFt dF∞−∞ w(t)e−j2πFt dt2.∑ν a ν w ν (t) ←→ ∑ ν a ν W ν (F )3. w ∗ (−t) ←→ W ∗ (F )4. W(t) ←→ w(−F )5. w(at) ←→ 1 W ( )F|a| a6. w(t − t 0 ) ←→ W (F ) · e −j2πFt 07. w(t) · e j2πF 0t←→ W (F − F 0 )8. w ∗ (t) ←→ W ∗ (−F )9.d n w(t)dt n ←→ (j2πF) n W (F )10.∫ t 1−∞ w(τ)dτ ←→j2πFW (F )omW (F )=0för F =011. −j2πt w(t) ←→ dwdF12. w 1 (t) ∗ w 2 (t) ←→ W 1 (F ) · W 2 (F )13. w 1 (t) · w 2 (t) ←→ W 1 (F ) ∗ W 2 (F )14.15.∫ ∞−∞ |w(t)|2 dt = ∫ ∞−∞ |W (F )|2 dF∫ ∞−∞ w 1(t) · w 2 (t)dt =∫ ∞−∞ W 1(F ) · W ∗ 2 (F )dFParsevals relationw 1 (t), w 2 (t) reella16. δ(t) ←→ 117. 1 ←→ δ(F )18. u(t) ←→ 1j2πF + 1 2 δ(F )19. e −at u(t) ←→ 1a+jΩ46