2008-3-21
A B C
D
4
1/2 1/4
1-1
[
]
1/8
1/8
HX
()log
E
1
p X
(
)
1
8
log2log4log8log8
111
248
3
113
8
228
31 (bits)
4
0
1
X
0
1
0.5
0.5
1
Y
0
1
1-3
[
]
1/2
1
X
pXp X
(0)(1)0.5
(0)(1)0.5
(0)(1)0.5
(0)(1)0.5
(0)(1)0.5
(0)(1)0.5
(0)(1)0.5
(0)(1)0.5
pYXpY
X
(0|0)(1|0)0.5
(0|0)(1|0)0.5
(0|0)(1|0)0.5
(0|0)(1|0)0.5
(0|0)(1|0)0.5
(0|0)(1|0)0.5
(0|0)(1|0)0.5
(0|0)(1|0)0.5
(0|0)(1|0)0.5
(0|0)(1|0)0.5
(0|0)(1|0)0.5
(0|0)(1|0)0.5
(0|0)(1|0)0.5
(0|0)(1|0)0.5
(0|0)(1|0)0.5
(0|0)(1|0)0.5
(0|0)(1|0)0.5
0
0
1
Y
Y
pY
X
(0|1) 0
(0|1) 0
(0|1) 0
(0|1) 0
(0|1) 0
(0|1) 0
(0|1) 0
(0|1) 0
(0|1) 0
(0|1) 0
(0|1) 0
(0|1) 0
(0|1) 0
(0|1) 0
(0|1) 0
pY
X
pY
X
(1|1) 1
pXYpX
(0,0)(0,1)0.25
Y
pX
Y
(1,0) 0
pX
Y
(1,1)0.5
p Y
(0)0.25
p Y
(1)0.75
1
2
125 s
125 ss
IXY
(;)log
E
pX Y
)
(,
pXp Y
()( )
2
0.25log0.25log0.5log
0.250.250.5
22
0.50.250.50.750.50.75
2
0.250.250.25log310.5log 3
1.50.75log3 (bits)
2
2
I XYHXHX Y
(;)()(|
)
1(1)(|1)
pYHX Y
1
3
h
10.75
1.50.75log3 (bits)
2
=0.3113(bit)
hxxxx
x
()log(1)log(1
)
1-5
[
]
=
1/(12510 ) =
6
810
3
Baud
=
810log 4
3
=
1610
3
bits/s
bits/s
2
2-3
50Hz
( )x t
n
0
1, 4
4
n
0,
xnT
()1, 0
s
x
(0.005)
(1)
(2)
(1)
xtxkTWtkT
()()sinc2(
k
)s
sT
s
1
W
2
s
0.01( )
4
k
(0.005)sinc(0.5)sinc(0.5
x
)
k
k
1
sinc(0.5)sinc(4.5)
(2)
sin(0.5)sin(4.5 )
0.54.5
0.566
0.566
0.566
tkT k
sinc(),0,1, s
sinc(),0,1,
sinc(),0,1,
sinc(),0,1,
sinc(),0,1,
sinc(),0,1,
sinc(),0,1,
sinc(),0,1,
sinc(),0,1,
sinc(),0,1,
sinc(),0,1,
sinc(),0,1,
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
s
8
8
8
8
100
2
ExtdxxkT 2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
ExtdxxkT
ExtdxxkT
ExtdxxkT
ExtdxxkT
ExtdxxkT()(
ExtdxxkT()(
ExtdxxkT()(
ExtdxxkT
ExtdxxkT
ExtdxxkT
ExtdxxkT
ExtdxxkT
ExtdxxkT
ExtdxxkT
ExtdxxkT
ExtdxxkT
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
2-11
xttf t
()sinc()cos2
()sinc()cos2
()sinc()cos2
1
1
1
1
100
100100
k
0
( )y t
x ttftxttf t
()sinc()cos2()sinc()sin 2
0
ˆ
lx t
()sinc( )
t
httfthttf t
()sinc()sin2()sinc()cos2
2
0
ˆ
2
lhtt e
()sinc( )
2
j
2
1
httf t
()sinc()sin 2
2
0
0
0
ytyt e
()Re( )
l
jf t
2
0
y txth t
()()( )
ll
l
1
YfXfH f
)
()()(
l
ll
2
X f
(
l
)
H f
(
l
)
1
2
1
2
1
0
f
f
fj
(1)/0
fj
(1)/1
1
0
f
f
1
2
0
Y f
(
l
)
fj
(1)/2
0
f
fj
(1)/ 2
1
f
2
()(
1
y tYfedf
)
2
1
l
2
l
jft
2
1
2
0
1
1
j
j
j
j
2
2
2
2
2
2
t
sin11
sin11
sin11
sin11
sin11
sin11
sin11
sin11
sin11
sin11
sin11
ttt
ttt
ttt
ttt
ttt
ttt
ttt
22
22
22
22
22
22
22
22
22
22
j
j
j
j
j
j
j
t
t
t
t
t
4
4
4
4
4
4
4
4
4
4
4
4
42 2
4
42 2
4
4
4
2 2
2 2
2 2
2 2
2 22 2
j
j
j
j
j
j
j
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
sin(1cos)sin(cos1)
ttt
ttt
ttt
ttt
ttt
444
444
444
444
444
444
444
444
444
444
444
444
444
444
444
444
444
444
ttjt
(1
f edffedf
edffedf
edffedf
edffedf
edffedf
edffedf
edffedf
edffedf
edffedf
edffedf
edffedf
edffedf
edffedf
edffedf
edffedf
edffedf
)
jft
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
j
j
j
j
2
2
2
2
2
2
0
00
00
000
00
(1
1 (1
1 (1
(1
(1
1
2
2
jft
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
)
)
)
)
)
1sin(cos
1
1
1
1
1
1
1
1sin(cos
1
1sin(cos
t
sin(cos
sin(cos
sin(cos
sin(cos
sin(cos
sin(cos
sin(cos
sin(cos
sin(cos
sin(cos
sin(cos
sin(cos
sin(cos
sin(cos
sin(cos
sin(cos
sin(cos
sin(cos
t
t
t
t
t
t
t
2
2
2
2
2
2
2
2
2
2
222 2
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
t
1
y tttf t
()(1cos)sinsin(2
()(1cos)sinsin(2
()(1cos)sinsin(2
()(1cos)sinsin(2
()(1cos)sinsin(2
()(1cos)sinsin(2
()(1cos)sinsin(2
()(1cos)sinsin(2
()(1cos)sinsin(2
()(1cos)sinsin(2
()(1cos)sinsin(2
1
1
1
1
1
1
1
t
2 2
4
4
)
)
)
)
)
)
)
)
)
)
)
1
1
1
1
1
1
1
4
4
t
1
2 2
t
0
2-19
( )t
t
()2cos(2
t
)
P
P
(0)(/2)1/ 2
[()]E
t
R
(0,1)
EtPtP
t
[()](0)2cos(2)()2cos(2
)
cos(2)sin(2 )
t
t
2
2
2
cf
B
R
(0,1)[2cos2cos(2)]
E
P
P
(0)4()4coscos
2
5
22
2
P2-25
0 / 2N
|H(f)|
B
-fc
B
fc
f
0
P2-25
2-25
1
2
PfH f
()(
N
)
N
0
2
2
N
0
2
2
2
2
2
2
0
f
f
f
f
f
f
f
f
f
f
c
c
c
f
f
fc
f
f
f
c
c
B
BB
2
2
2
2
2
2
B
B
2
R
()(
()(
()(
()(
()(
()(
()(
()(
()(
()(
)
)
)
)
)
)
)
)
)
)
Pfedf
NNPfedf
Pfedf
Pfedf
Pfedf
Pfedf
N
NN
j
j
j
j
2
f
f
f
f
NBB
00NBB
NBB
0
00
f
f
f
sinc()cos(2
sinc()cos(2
sinc()cos(2
sinc()cos(2
sinc()cos(2
sinc()cos(2
sinc()cos(2
sinc()cos(2
sinc()cos(2
sinc()cos(2
) c
)
)
)
)
)
)
)
)
)
0
0
1
2
2
f n
N
()exp
2
0N B
2
n
2
2
2-30
( )t
[
]
Yttt T
()()(
)
R
( )
P2-30
3
EYtYtEttTtt
[()()][(()())(()())]
12112
T
2
EttEtT
t
[()()][()()]
121
EttTEtTt
T
[( )()][()()]
121
RRTR
T
2()()(
)
PfRRTR
Y
T
()[2()()()]
Pfe
()(2
PffT
2()(1cos2
jfTjfT
2
e
)
2
2
2
)
2-35
( )X t
( )Y t
YtXtftXtf t
()()cos(2)()sin(2
0
ˆ
)
0f
[0,2 ]
P2-35
( )Y t
PX( f )
A
-B
ˆ
YtXtX t
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
()()cos()sincos2
XtXtf t
X ()sin()cossin 2
X ()sin()cossin 2
tXtf t
tXtf t
XX ()sin()cossin 2
XX ()sin()cossin 2
tXtf t
tXtf t
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
()sin()cossin 2
ˆ
ˆ
B
f
ff
0
P2-35
f t
0
0
ZtXtX t
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
()()cos()sin
ˆ
ˆˆ
ˆˆˆ
ˆˆˆ
ˆˆˆ
ZtXtXtXtX t
()()cos()sin()sin()cos
()()cos()sin()sin()cos
()()cos()sin()sin()cos
()()cos()sin()sin()cos
()()cos()sin()sin()cos
()()cos()sin()sin()cos
()()cos()sin()sin()cos
()()cos()sin()sin()cos
()()cos()sin()sin()cos
()()cos()sin()sin()cos
ˆ
ˆ
ˆ
ˆ
YtZtftZtf t
()()cos2()sin 2
ˆ
0
YREYtY t
()()(
)
R
Z
fR
()cos2()sin 2
0
ˆ
Z
RR
()()cos()sin
ZX
2
R
X
0
f
2
0
EXtX t
()()cossin()()cossin
ˆ
XR
( )
4
0
( )X t
( )X t
ˆ
EXtX t
PfP f
)
Z
()(
X
PfF R
()( )
Y
Y
PffPf
()(
Z
f
0
)
2
Z
0
jfP f
sgn()(
)
Z
fff
()(
f
0
)
j
2
0
Pf
Z
(
0
)
1sgn(
f
2
f
Pf
()
Z
PffBff
()
Z
0
f
0
00
f
f
)
0
)
0
Pf
Z
(
f
2
1sgn(
f
f
)
0
fff B
0
0
ff
0
f
0
PX( f )
A
f0
f0+B
[-1, 1]
-B0
B
f
PY( f )
A
-f0-B
-f0
2-37
X(t)=A+Bt
)=)=AA)=)= ++BtBt++
XR t
t
(,
(,
(,
XX (,
(,
(,
)
)
)
)
)
)
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
Xm t
( )
A B
AA BB
( )X tABt
( )( )XX tABt
tABt
( )( )( )tABt
tABt
tABt
tABt
tABt
tABt
EXtEAEBt
EXtEAEBt
EXtEAEBt
EXtEAEBt
EXtEAEBt
EXtEAEBt
( )
0
0
0
XR ttEABtABt
(,)()(
1
2
)
1
2
EAEBt t
2
2
1 2
1 (1
3
t t
1 2
)
5