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Human Systems Lab., Dept. of Systems Science Graduate School of Informatics, Kyoto University

#2

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l l l l l l l

Copyright 2012-2015 Manabu Kano. All rights reserved. 2

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3

Fourier (17681830)

4

sin x, cos x 2

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y

sin

0 2x

y1

1

-1

-1

5

1

= 1 rad

sin

cos

6

2 sin x, cos x

1

1

-1

-1

20

2

-3 -2 -1 0 1 2 3

Copyright 2012-2015 Manabu Kano. All rights reserved. 4

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7

f (x) g(x) T h(x) T

f (x) g(x) T h(x) T

8

f (x) T c

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Outline 9

l l l l l l l

10

2 f (x) g(x)

f (x) g(x)

a b aTb = 0

ab

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11

Outline 12

l l l l l l l

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(1) 13

f (x) cos mx

( a0 )14

f (x) cos mx (m=0)

a02

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(2) 15

f (x) sin mx

Outline 16

l l l l l l l

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17

x

f (x)

x

f (x)

(1) 18

f (x)

f (x)

x

f (x)

x

f (x)

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(2) 19

l

l

20

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21

2 sin x, cos x

-1

0

1

0 -

Outline 22

l l l l l l l

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(1) 23

fe(x) bn= 0

fe(x) sin nx

(2) 24

fo(x) an= 0

fo(x) cos nx

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25

2 f (x) g(x) an( f ), bn( f ) an(g), bn(g)

cf (x)+dg (x) can( f )+dan(g), cbn( f )+dbn(g)

Outline 26

l l l l l l l

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27

x 2--2 0

f (x)

x 2--2 0

f (x)

28

x 2--2 0

f (x)

x2

--20

f (x)

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29

30

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31

32

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33

34

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Outline 35

l l l l l l l

36

1.

2. x =