Tajzie2
10
) :( / : ) : ( : : : : : : : , , , , ) ,( , , , [ ] [ ] [ ] { } 1 4 k n n k n k δ δ ∞ =−∞ = − − − − ∑ [ ] [ ] [ ] { } 4 k x n n k n k δ δ ∞ =−∞ = − − − ∑ [ ] [ ] [ ] { } 1 4 k x n n n k δ δ ∞ =−∞ = − − − ∑ [ ] [ ] [ ] { } 0 1 4 k n n n k δ δ ∞ = = − − − ∑ 1 - . . . . [ ] [ ] [ ] 1 4 x n u n u n = − − ( ) 2 1 sin 2 x t t = [ ] [ ] [ ] 3 3 x n u n u n = − − ( ) 4 1 cos 2 x t t = 2 - . . . . ( ) x t ( ) sin(3 ) t x t e t π − = + ( ) { } Re cos 3 2 t x t e t π = + ( ) { } Re cos 3 4 t x t e t π − = + ( ) { } Re cos 2 4 t x t e t π − = + ( ) { } Re cos 3 2 t x t e t π − = + 3 - . . . . 1 10 1391-92 /
Transcript of Tajzie2
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[ ] [ ] [ ]{ }1 4k
n n k n k δ δ ∞
=−∞
= − − − −∑
[ ] [ ] [ ]{ }4k
x n n k n k δ δ ∞
=−∞
= − − −∑
[ ] [ ] [ ]{ }1 4
k
x n n n k δ δ ∞
=−∞
= − − −∑
[ ] [ ] [ ]{ }0
1 4k
n n n k δ δ ∞
=
= − − −∑
1
-
.
.
.
.
[ ] [ ] [ ]1 4 x n u n u n= − −( )2
1sin
2 x t t
=
[ ] [ ] [ ]3 3 x n u n u n= − −( )4
1cos
2 x t t =
2
-
..
..
( ) x t
( ) sin(3 )t x t e t π
−= +
( ){ }Re cos 32
t x t e t π
= +
( ){ }Re cos 34
t x t e t π −
= +
( ){ }Re cos 24
t x t e t
π − = +
( ){ }Re cos 3
2
t x t e t
π − = +
3
-
..
..
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10( ) j t x t je=( )1
( ) j t
y t e − +
=
( ) j n z t e π
=)sin()( t t y =
4
-
..
..
x[n]n<2 , n>4 ,x[-n+2]
5
-
..
..
x(t)t<3 ,+ x(2-t)x(1-t)
2t > −2t >2t < −2t <
6
-
....
[ ] 3 13 ( ) / 5
2
j x n e nπ = +
2051015
7
-
....
.
[ ] [ ] [ ]. 2 y n x n x n= −
8
-
....
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mmmm .
[ ] [ ]n m
k n m
y n x k +
= −
= ∑
9
-
..
..
2( ) ( 1) y t t x t = −
10
-
..
..
x(t-1) x(2t+1) 11
-
..
..
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x(t-1) , x(t) + x(-t).u(t) 12
-
..
..
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x[n] .x[3n+1] 13
-
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x[n] .x[3-n] 14
-
..
..
( ) 2 5
2 cos 4sin( )3 3
x t t π π
= + +
5 5 0 2 2
12 , 0 ,
2a a j a a a− −
= = − = = =
5 5 0 2 2
12 , 0 ,
2a a j a a a− −= = = = =
0 2 2 5 51
2 , , 22
a a a a a j− −
= = = = = −
0 2 2 5 51
2 , , 22
a a a a a j− −
= = = = =
15
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( ) 2 5
2 cos 4sin( )3 3
x t t π π
= + +
0 0, 23
w aπ
= =0 0, 03
w aπ
= =0 0, 22
w aπ
= =0 0, 02
w aπ
= =
16
-
....
( ) x t
{
0
1/ 5, 0 11/ 5, 1 2
w
( ) t
t x t
π
≤ <
− ≤ <
=
=
23sin
2
jk
k
k a e
k
π
π
π
−
=
22sin
2
jk
k
k a e
k
π
π
π
−
=
22sin
2
jk
k k
a ek
π
π
π
=
22sin
4
jk
k k
a ek
π
π
π
=
17
-
..
..
1x (t)wwww 1 k a. :
2 1 1( ) (1 ) ( 1) x t x t x t = − + − 2x (t)
1
1 2
2
w
( ) jw k
k k k
w
a e a a−
−
=
= +1
1 2
2
w 2
( ) j w k
k k k
w
a e a a−
−
=
= +
2
1 2
2
w 2
( ) j w k
k k
w
a e a−
=
=1
1 2
2
w
( ) j w k
k k
w
a e a−
=
=
18
-
..
..
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zzzz x[n]
[ ]1
x[n]= 35
n
u n
−
3
1
1 1
1125 513
z z
z
−
−
>
−
1
1
1 1
1125 513
z z
z
−
−
>
−
1
1
1 1
1125 31
3
z z
z
−
−
>
−
1
1
1 1
125 31
3
z z
z
−
−
>
−
19
-
..
..
zzzz
1
1 1
11
3( ) 2(1 )(1 2 )
z
X z z z z
−
− −
−
= >
− +
[ ] [ ] [ ]1 8
(2)9 9
n X n u n u n= +
[ ] [ ] [ ]
2 7(2)
9 9
n X n u n u n
−= +
[ ] [ ] [ ]1 8
( 2)9 9
n X n u n u n= + −
[ ] [ ] [ ]2 7
( 2)9 9
n X n u n u n= + −
20
-
..
..
( )t
2 1( )
t x t e
− −=
2( )
4
jwe
x jww
−
=
+
4( )
4
jwe
x jww
=+
2
4( )
4
jwe x jw
w
−
=
+
4( )
4
jwe x jw
w
−
=+
21
-
..
..
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x(jw) .
( ) {2 , 0 jw2 ,X e
j w j w
π
π π
< ≤
− − < ≤=
24( )sin ( )
2
n
n
π
π −
24( )sin ( )
4
n
n
π
π −
24( )sin ( )
4
n
n
π
π
24( )sin ( )
2
n
n
π
π
22
-
..
..
X(t)X(s) X(t+T)
X(s/T)X(Ts)-sTe X(s)sTe X(s)
23
-
....
LTI .
Re {s} <-1
( ) 3 2
H S 3( 1)( 4)
S
S S
−= +
+ −
43 ( ) ( ) 2 ( )t t t e u t e u t δ
−− − − −
4( ) 2 ( )t t e u t e u t −
− − −
42 ( )t t e e u t − − −43 ( ) 2 ( )t t e u t δ − −
24
-
..
..
x(t) y(t)
.
))(sin()( t xt y =
1-
,
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]y[n] = x[n] *h[ n[
[ ] [ ] [ ]
[ ] [ ] [ ] [ ]
h n 2 1 2 1
2 1 3
n n
x n n n n
δ δ
δ δ δ
= + + −
= + − − −
2-,
.
2( 1) ( 1)
sin(2 / 4)
t u t e
π π
− − −
+
3-,
zzzz ( ) x t . .
1
1 1
11
3( ) 2(1 )(1 2 )
z
x z z z z
−
− −
−
= >
− +
4-,
.
5
( ) sin(2 ) ( )
( ) ( 1)
t
t
x t e t u t
x t e u t −
= −
= −
5-,
1010 1391-92 /
