X
傅里叶复指数级数证法 2
00
1
( ) c o snn
n
x t A A n t
由欧拉公式:
00j ( ) j ( )
0
1c o s ( ) ( e e )
2
nnn t n t
nnt
00j( ) j( )
0
1
1( ) ( e e )
2
nnn t n t
n
n
x t A A
00j j j j
0
1
1 ( e e e e )
2
nnn t n t
n
n
AA
X
00j j j j
0
11
11e e e e
22
nnn t n t
nn
nn
A A A
0j1 e
2
nt
nA
000 j j0
0
11
1 ee
2
nj t n tj
n
nn
A e e A
00 00 jt jA e e 0j( ) j
1
1 ee
2
nnt
n
n
A
0jj
1
1 ee
2
nnt
n
n
A
傅里叶复指数级数证法 2
je n?
0j( ) e nt
n
n
x t c?
0
0,0
,0
2
n
j
n jn
A e n
c A
en?
令,得 00||
1
| |,0
2nn
CA
C A n
傅里叶复指数级数证法 2
00
1
( ) c o snn
n
x t A A n t
由欧拉公式:
00j ( ) j ( )
0
1c o s ( ) ( e e )
2
nnn t n t
nnt
00j( ) j( )
0
1
1( ) ( e e )
2
nnn t n t
n
n
x t A A
00j j j j
0
1
1 ( e e e e )
2
nnn t n t
n
n
AA
X
00j j j j
0
11
11e e e e
22
nnn t n t
nn
nn
A A A
0j1 e
2
nt
nA
000 j j0
0
11
1 ee
2
nj t n tj
n
nn
A e e A
00 00 jt jA e e 0j( ) j
1
1 ee
2
nnt
n
n
A
0jj
1
1 ee
2
nnt
n
n
A
傅里叶复指数级数证法 2
je n?
0j( ) e nt
n
n
x t c?
0
0,0
,0
2
n
j
n jn
A e n
c A
en?
令,得 00||
1
| |,0
2nn
CA
C A n