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陳正宗終身特聘教授SERIES SUM USING Parseval’theorem

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陳正宗終身特聘教授 SERIES SUM USING Parseval’theorem

系級: 學號: 姓名:

0 1

( ) , 0 , ( ) ( cos( ) sin( ))

0, 0

n n n

t t

f t f t a a nt b nt

t

  

         

(1) 求 , , 。

(2) n 取多少時， 有 95%的準確度。

(Parseval’s 定理) ,

延伸閱讀：J.T. Chen, S.W. Chyuan, D.W. You, F.C. Wong, Normalized quasi-static mass - A new definition for multi-support motion problems (1997) Vol. 26, pp.129- 142. Finite Elements in Analysis and Design. (SCI and EI) (Fourier 好好學，可以應 用在地震工程上)

2014/05/06 Fourier-sum 檔名: ).doc 怡絹製表

95%

N=6 時就符合規範 a

0

a

n

b

n

2

( ) f t dt

0

4

a

2

1 cos( )

n

a n

n

  

2

cos( )

n

n n

b n

 

 

2 2 2 2

0 1

( ) [2 (

n n

)]

n

f t dt a a b

   

3 2

( ) f t dt 3

N 10

f t dt

2

( ) [2 a

02

nN1

( a

n2

b

n2

)] F N ( )

0 2 4 6 8 1 0 N

0 2 4 6 8 1 0

F  N

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