Serie De Fourier

  • June 2020
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Una función f(t) con periodo 2π está definida dentro del periodo 0    2  0     2         2

       2 2

  2

Dibuje la grafica de la función f(t)para 2    3 y encuentre la expresión en serie de Fourier para ella:

 

2      

  2         !         2 2  2 

   

1   /2 # |  2 0





  | 2 /2

 & 

  2 (| 4 

1     #    2         2 4 4  8

   +

14 , 8

 

5  8

. 

2    cos 23    

)

)

  2   1  .  cos 2     cos 2     cos 2 !   cos 2     2 2  2   

INTEGRAL DE TABLA   cos 2  

  sen 2   PROPIEDADES cos 22  1

cos 2  1. sin 22  0 sin 2  0

1 4sin 2  2 cos 27 2

1 4cos 2  2 sen 27 2

. 

1  2 1 2 1   1 1   cos   9:2     1. , + 9:2  22 2 2 2 2 22 2 22 22

;. 

2    sen 23   

. 

2 3 1 1   1. , +cos  2 2 2 2



  2   1  sen 2     sen 2     sen 2 ! ;.    sen 2     2 2  2  

;.  ;.  ;. 



  1 1 sen 2  2 cos 2 2  1 2  # |  cos |  0   sen 2  2 cos 2| ) 2    2 2 2 2 22 2 0 1 1 2 2  2  cos 22  0=  cos , +  <sin  2 2 2 22 2 1 1 2 2  2 cos +  <sin < =  =  ,  2 2 2 22 2

SERIE DE FURIER  

>  ?@

 ∑H .I? B.C Dcos ?

. 

    1. FG  ∑H .I? B D<.C <sin <  =  E

?

?

?

.

.  . =  . cos  =FG sin 2 

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