5 Ejercicios Series Fourier
6
Ejercicio 1 Calcular la serie compleja de fourier para : < < → − < < → = seg t seg t t f 2 1 4 1 0 4 ) ( f (t+2) = f (t) ⇔ T=2 ⇔ ω 0= π rad/s ∑ ∞ −∞ = ⋅ ⋅ ⋅ ⋅ = n t n j n o e C t f ω ) ( ( ) ( ) ( ) n n j n j n j t n j t n j n t n j t n j T T t n j n n n j n e n j e n j e dt e dt e C dt e dt e dt e t f T C o o o o o ) 1 ( 0 cos sen cos 1 2 1 ) 2 ( 2 ) 2 ( 4 2 1 4 2 1 ) ( 1 0 1 1 0 0 1 1 0 2 / 2 / − = + ⋅ = ⋅ ⋅ + ⋅ = ⋅ ⋅ − − ⋅ + ⋅ ⋅ − − ⋅ − = ⋅ ⋅ + ⋅ ⋅ − = = ⋅ ⋅ ⋅ + ⋅ ⋅ − ⋅ = ⋅ ⋅ ⋅ = ⋅ ⋅ − ⋅ ⋅ − ⋅ ⋅ − − ⋅ ⋅ ⋅ − ⋅ ⋅ ⋅ − − ⋅ ⋅ ⋅ − ⋅ ⋅ ⋅ − − ⋅ ⋅ ⋅ − ∫ ∫ ∫ ∫ ∫ π π π π π π π π ω ω ω ω ω ( ) ( ) ar n n C parell n n j ar n n j C n n n sen º 90 8 0 8 sen 1 1 4 2 2 2 ∀ ⇔ − ⋅ = = ⋅ ⋅ = ⇒ − − ⋅ ⋅ ⋅ = π π π
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ejercicios ecuaciones diferenciales fourier
Transcript of 5 Ejercicios Series Fourier
Ejercicio 1
Calcular la serie compleja de fourier para :
f (t+2) = f (t) T=2 0= rad/s
Ejemplo2:Aplicaciones en circuitos, de forma senoidal
la serie de fourier tiene el siguiente aspecto
a0 / 2 valor medioa1, a2, b1, b2, ... coeficientes de Fourier0 ... frecuencia (2 /T)n 0 ... harmnicos
Ejemplo 3:
f(t)=2sen t sen(2t) + (2/3)sen (3t) - 1/2sen (4t) +2/5 sen (5t)+....
Ejemplo 4:
Entonces; tenemos el siguiente procedimiento
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Analticamente tenemos: