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陳正宗終身特聘教授

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2014/05/06 Fourier-sum檔名: ).doc 怡絹製表

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

a0

,

an

,

bn

(2) n 取多少時,

f2

( )

t dt

有 95%的準確度。

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

(Parseval’s 定理)

3 2( ) f t dt 3

,

2 02 2 2

1

10 ( ) [2 ( )] ( )

N

n n

n

N f t dt a a b F N

0 2 4 6 8 10

N 0

2 4 6 8 10 F N

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)

95%

N=6 時就符合規範

參考文獻

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