plh22 - 2009-2010-oss2
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22
2
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To
(Baseband Communication)
(Bandpass Communication) T
.
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: To
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DSB To x(t)
cos2fct yDSB (t)=x(t)cos2fct
:
Y[f]=0,5X(f-fc)+0,5X(f+fc)
f>fc f
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DSB
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DSB
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xDSB(t)
xDSB(t)
cos2fct ,
,
.
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.
m
.
.
-
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Y[f]=0,5X(f-fc)+0,5X(f+fc)
0,5 Y(f-fc) + 0,5 Y(f+fc) =
X(f-2fc) + X(f) + X(f+2fc)
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x(t)=Ac[1+x(t)]cos2fc
t=A(t)cos2fct
(t):
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A(t)
x(t).
DSB ,
.
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Y
[f]=F{[A+x(t)]cosct}=F{Acosct}+F{x(t) cosct}=
0,5 {(-c)+(+c)}+0,5{(-c)+(+c)}
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+x(t) >0=> >=|min{x(t)}|
x(t)
H
RC
1/fc1
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+x(t) >0=> >=|min{x(t)}|
x(t)
H
RC
1/fc1
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DSB, AM,
,
.
,
.
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AM
C,
AM.
AM ,
R,
.
AM , -
, .
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, .
R, C.
.
AM .., .
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(SSB) DSB AM
,
.
, ,
.
DSB AM
.
,
,
.
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(SSB) SSB
() DSB
()
.
3.12 ,
, SSB.
BPF
, .
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(SSB)( )
( )
( )
( )
f
f
f
f
( )X f
xfxf
( )D SBX f
cfcf
cfcf
( )B P FH f
( )S SBX f
cfcf
.
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SSB
.
3.13
SSB .
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SSB
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SSB
, ,
SSB.
(vestigialsideband VSB).
VSB , , .
VSB
, .., (facsimile).
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i
S
( )o
S N
DSB 2x
f 21
2c xA S
i
x
S
f
AM
2x
f ( )
211
2c xA S+
22
i c
x
S A
f
AM ,
( ) 1iS N
2x
f ( )2 21
12
c xA S+ 2
2i c
x
S A
f
SSBx
f 21
2c xA S
i
x
S
f
SOSSOS
.. 3.73.7
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.
, .
.
.
3.7 4 2, 2004
db, db
1 &
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1: &
, x(t) , c c .
c( ).
() x(t) ,
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() y(t)
Fourier.
y(t)=x2(t)
, x (t) &x2(t)
2 2 2 2( ) ( ) [1 ( )] cosc c ct ax t aA x t t = = + =
2 22 2 2 2
2 2 2 22 2 2 2
1 1[1 ( )] ( cos2 ) [1 ( )] [1 ( )] cos22 2 2 2
cos2 ( ) ( ) ( )cos2 ( )cos2
2 2 2 2
c cc c c
c c c cc c c c
aA aAaA x t t x t x t t
aA aA aA aAt aA x t x t aA x t t x t
ct
+ + = + + + =
+ + + + +
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() ()
Fourierx(t)
sinc
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() ()
x2(t)
[ ]
[ ]
2 2
2 2
2 2 2
2
2
2
( )
2 2
cos 2 ( 2 ) ( 2 )2 4
( ) ( ) 2
( )cos 2 ( 2 ) ( 2 )2
2 22 2 2
Fc c
Fc c
c c c
F
c c cx
F c
c c c c
c c c
x x
aA aAf
aA aAt f f f f
f
aA x t aA X f aA rect f
aAaA x t t X f f X f f
aA f f f f rect rect f f
+ +
=
+ + =
++
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() ()
x2
(t)
( ) ( ) ( ) ( )F22 2( ) sin 2 t ( )
42 = 2 rectx x
x
x t c f G ff
ff X f X f f f
x
= =
{ }
( ) ( )
{ } ( ) ( ) ( ) ( )
2 22 2
2
2 2
2 2 2
2 2
2
( ) ( )2 2
2 , 222
2 2 4
0, 2
( )cos 2 ( )cos 2 2 2 2 22 2 4
2 24
Fc c
c
x xc c
x
xx
Fc c c
c c c c c c
cx c
aA aAx t F x t
aAf f f faA aA f
X f X f f f rectf
f f
aA aA aAx t t F x t t X f f X f f X f f X f f
aA f f f
=
= = =
>
= + + + =
= 2 22 24 4c c
x c
x x
f f f frect f f f rect f f
+ + +
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() ()
-2c 2c
-2c- x -2c+ x 2c- x 2c+ x
-2c- 2x 2c+ 2x2c- 2x-2c+
2x
-2x -x x 2x
|Y(f)|
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() () |x(t)|
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2 3, 2005
.
2: &
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2: &
.
xc(t)=cos(2fct) [f1=30kHz, f2=40kHz, f3=20kHz, fc=1MHz]. (A) DSB ,
Fourier .
(B) SSB .
() 60 KHz xc(t)=cos(2fct) [fc=1 MHz] DSB, AM, SSB. .
() () 30dB
n/2=10-9 W/Hz. (DSB, SSB, AM ) 45 dB.
( ) ( ) ( ) ( )tftftftx 3212 2cos2cos2sin
2
1 +=
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()
(A) DSB , Fourier .
1.
f =60kHz f=20kHz
( ) ( ) ( ) ( )
( )[ ] ( )[ ] ( )[ ]{ }
( )[ ] ( )[ ]tftf
tfftfftf
tftftftx
LH
2cos2
12cos
2cos2cos22cos
2
1
2cos2cos2sin2
1
32321
321
2
+=
=+++=
=+=
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() ()
2. DSB
DSB
( ) ( )[ ] ( )
( ) ( ) ( )
( ) ( )( ) ( )( ) ( )( ) ( )( )tfftfftfftfftf
tftftf
txtxtx
LcLcHcHcc
LHc
cAM
++++++=
=
++=
=+=
2cos4
12cos
4
12cos
2
12cos
2
12cos
2cos2
1
2cos12cos
1
( ) ( ) ( )
( ) ( ) ( )
( )( ) ( )( ) ( )( ) ( )( )tfftfftfftff
tftftf
txtxtx
LcLcHcHc
LHc
cDSB
+++++=
=
+=
==
2cos4
12cos
4
12cos
2
12cos
2
1
2cos2
12cos2cos
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() ()
2. DSB
DSB
( )( ) ( )( ) ( )( ) ( )( )( ) ( )( ) ( )( )( )
( )( ) ( )( )( ) ( )( ) ( )( )( )LcLcLcLc
HcHcHcHccc
AM
ffffffffffff
ffffffffffffffff
fX
++++++++
+++++++++++==
8
1
8
1
4
1
4
1
2
1
( )
( )( ) ( )( )( ) ( )( ) ( )( )( )
( )( ) ( )( )( ) ( )( ) ( )( )( )LcLcLcLc ffffffffffff ++++++++
HcHcHcHc
DSB
ffffffffffff
fX
++++++++=
=
4
1
4
1
4
1
4
1
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() ()
3. DSB
DSB
1000 1020 1060940 980-1000 -980 -940-1060 -10200
1/8
1/4
1/2
f(kHz)
1000 1020 1060940 980-1000 -980 -940-1060 -10200
1/8
1/4
1/2
f(kHz)
1000 1020 1060940 980-1000 -980 -940-1060 -10200
1/8
1/4
f(kHz)
1000 1020 1060940 980-1000 -980 -940-1060 -10200
1/8
1/4
f(kHz)
fc=-1000KHz f c=1000KHz
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()
(B)
SSB . DSB
:
980 kHz 1020 KHz.
[940kHz, 980kHz]
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(B) ()
o SSB SSB
1000 1020 1060940 980-1000 -980 -940-1060 -10200
1/8
1/4
f(kHz)
1000 1020 1060940 980-1000 -980 -940-1060 -10200
1/8
1/4
f(kHz)
fc=-1000KHz f c=1000KHz
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()
() 60 KHz
xc(t)=cos(2fct) [fc=1MHz] DSB, AM, SSB.
. DSB
W=2fx=120kHz.
SSB W=fx=60kHz
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()
() ()
30dB
n/2=10-9 W/Hz. (DSB, SSB, AM
)
45 dB.
() ()
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() ()
BPF
( )DSB t
cos2 cf t
( ) ( )SS Bx t n t+
PF
)(tn
)(tyo)(ty i
)(tx
LPF
cos2 ct
( )SS Bx t
BPFBPF 22ffxx,,,,
,, ffcc,,
SSxx
SSii,N,Nii SS00,N,N00
SNR=10logSNR=10log1010(S/N)(S/N)
((--n) dB=10logn) dB=10log1010(S(Safterafter/S/Sbeforebefore))
SSafterafter/S/Sbeforebefore=10=10((--n)/10n)/10=>=>
SSii/S/Sxx=10=10((--n)/10n)/10
-30db
.
Sx
-30db
Si
45db
() ()
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( ) ()
() () DSB
SNR45db10log10(Si/nfx) 45 (Si/nfx)
104.5
n=2*10-9 W/Hz, fx=60KHz Si 2 * 10
-9 * 60000* 104.5 Watts= 12 * 10-5 * 104.5
Si
Sx 30db, SNR(Si/Sx)=-30 db 10log10(Si/Sx) =-30 (Si/Sx)=10
-3
Si= 10-3 * Sx
Si= 10
-3
* Sx 12 * 10-5
* 10
4.5
Sx 12 * 10
-2 * 104.5 =3,79 Kw
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,
[ ]( ) cos 2 ( )c c cx t A f t t = +
(t) x(t).
,
.
.
,
(t) x(t):
(phase modulation PM)
(frequency modulation FM).
PM
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FM
( ) cos ( )PM c c px t A t k x t = +
kp: .
( ) cos ( )t
FM c c fx t A t k x d
= +
kf: .
A. (PM).
. (FM).
((t)t)
x(t)x(t)
dd((t)/dtt)/dt
x(t)x(t)
PM FM
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cos PM
( )sin FM
p x x
f x
x
x
k A t
t k At
=
( ) cosx xt A t=
[ ]( ) cos sinFM c c xx t A t t = +
f x
x
k A
=
p xk A =
{ }max i cx x
= = ==f/ff/fxx
ff
22,,
77
20042004
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( ) ( )2 1 2 1x xW f + = +
77
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( 7, 2 2004)
Acos(20t) [cos(10t)]2 A/2
[sin(20t)]2 Asin(30t)sin(10t) FM
6.0 6.06 MHz .
,
40 KHz 80
KHz .
.
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( 7, 2 2004)
A cos(20 t) [cos(10 t)]2 A/2 [sin(20 t)]2 A
sin(30 t) sin(10 t)
= A cos(10 t) [cos(20 t) cos(10 t) - sin(20 t) sin(10 t)] - A sin(30 t) sin(10 t)
= A cos(30 t) cos(10 t) - A sin(30 t) sin(10
t) =A cos(40 t) fx=20 KHz
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( 7, 2 2004)
fx = 20 Hz
.
40 KHz 80 KHz
, 1 = / x = f / fx = 40 KHz/ 20 Hz = 2000
2 = / x = f / fx = 80 KHz/ 20 Hz = 4000
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( 7, 2 2004)
W1 = 2 (1+2000) fx = 80.04 KHz. ( 3.49 KHz).
W2 = 2 (1+4000) fx = 160.04 KHz
( )2 1 xW +
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( 7, 2 2004) X ,
. 6z
FM (6000-40.02, 6000+ 40.02) KHz = (5959.98,6040.02) KHz
6,06 z=6060 KHz
FM (6060-80.02, 6060 + 80.02) KHz = (5979.98,
6140.02) KHz.
(5959.98, 6140.02) KHz = 180.04 KHz
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Parserval
,
Parseval, P = = (
Parseval .3 .83 .
& )
=
. 2, 7, 2005
dttx+2|)(|
22| ( ) | kX f df a
+
=
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f2 ( )X f
f3( )X f
f
1( )X f 1( )x t
2 ( )x t
3( )x t
1cf
2
cf
3cf
f1c
f2c
f3c
f
1cf
2cf
3cf
1( )x t
2( )x t
3( )x t
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,
.
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T ... , .., , ,
. , , .., , , .
.. , .
.
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-
.
A/D (Analog to Digitalconversion) .
:
(Pulse Code Modulation PCM) .
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-
, , .
A/D , .
.
.
:
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x(t), fx,
x(nT), n=1,2, ,
T
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: () x(t), ()
(t), Ts , ()
x(t)=x(nTs), n=1, 2, , .
::
x(t)=x(nTs), n=1, 2, ,
x(t)=cos(2t)sin(t/2)x(nTs)=cos(2nTs)sin(nTs/2)
fs=1000 Hz,
s=1/1000,
x(nTs)=cos(2n/1000)sin(n/2*2
000)
0
x(t)
t0
(t)
ts 2s 3s 4s 5s 6s 7s
t0
xs(t)
()
()
()
Ts
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: () X(f) x(t), () Xs(f)
xs(t), , fs>2fx,
() Xs(f), fs
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(Low-pass)
f=0.
W
W fs-B
xs(t)
Xs(f)
y(t)=x(t)
X(f)
-W B B W fs-B
fs B x(t)
aliasimg
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fs 2 X(f-nfs) Xs(f), :
To
aliasing. aliasing
s(f)
-W W fs 2fs
-W W
Xa(f)
Nyquist
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Fourier.
Fourier
. 2, 5, 2005
.
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( 2, 5, 2005)
Nyquist
sinc2(100t)
.
,
(f) )(X(t) fxF
( ) ( )
( )
2
2
sin
1sin 100100 100
MF
MF
c t f
fc t
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1 ,
, 0
0,
xx ax x
tri aaa a
x a
>
-
x
( )x1
( ) ( )
2
2 sinsinFT a fx xtri a c f aa a a f
= =
1
100 100
f
=100
fmax=100 fs=2*fmax=200 Nyquist
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(
delta )
.
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: () x(t), () s(t) , ()
xs(t)
() x s(t), .
0
x(t)
t0
ts 2s 3s 4s 5s 6s 7s
()
()
t0
xs(t)
()
s(t)
Ts
t0
x's(t)
()
- Raised Cosine Pulse
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222 /41)/cos(
/)/sin()(
TtrTrt
TtTttx
=
=0.5
r = 0.35
1.35
To x(t)
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fs = 20 >> 2B = 2x1.35=2.70
To x(t)
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fs = 6 > 2B = 2.70
To
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liasing fs = 2.5 < 2B = 2.70
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: 300 Hz
4000 Hz
8000 samples/ sec.
:
15 kHz.
CDs 44.000samples/sec.
Video:
20
/sec
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.
.
.
PCM
PCM
K - Quantization
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Nyquist.
bits .
(Quantization) () bits.
O
(t)
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xq(t)
x(t)
xq(6Ts)xs(6Ts)
4.7 : )(tx
)(txq .
,..., 21 mm (
)( ss nTx )( sq nTx , ).
: .
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1 2 3 4 5 6 7 8 9 10 11 12 13 14
m1
m5
m4
m3
m2
1 2 3 4 5 6 7 8 9 10 11 12 13 14
m1
m5
m4
m3
m2
1 2 3 4 5 6 7 8 9 10 11 12 13 14
m1
m5
m4
m3
m2
() ()
() ()
4.8
: () , () , () , , () , .
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,
,
.
,
.
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4.9 4
x(t)
4.9
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4.9 )(tx .
a b , -. Q ,
Q
ab =
)(txq :iiiq xtxxmtx
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4.10 Gaussian.
( )+, 8 .
x(t)
( i ).
( ix )
( im ) -
.
.
,
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,
.
))(()( txgty =
)(tx )(ty , -
.
, )(ty .
(compressor), (expander).
( 1g )
)(tx .
compander (COMPressor expANDER).
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, ,
, .
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.
, , -
.
-
,
.
4 / . 4
)( tx [ ]4,4 .
sT
,...2,1),()( == nnTxtx ss .
)( tx q .
-
0, 1, 2, , 15.
4.1 4.12
.
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4.12 . .
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, ,
.
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sT
14 bits/sec.
P C M
, P C M -
.
, L ,
L2log .
, sf , -
Lfs 2log b its/sec .
-
2 bi ts /sec/H z, , PCMB , P C M
LfB sPCM 2log2
1
PCM
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.
(DPCM-Differential PCM)
.
bits
PCM
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() . DPCM (ADPCM
Adaptive DPCM) -
.
ADPCM 32kbits/sec , (.. DECT)
bits .
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(Differential PCM
DPCM), (bits).
, , .., .
,
, PCM-
.
, -
bit .
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)(tx
)( tx
)(ty
4.13 .
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)(1 tx)(1 tx
)(2 tx
)(2 tx
4.14
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0
)(tx
)( tx
)( tx
4.15
5:5:
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5:5:
(( ,,
))
::
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::
((unipolar):unipolar):
..
((bipolar):bipolar): g(t)g(t)
--g(t).g(t).
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..
..
..
..
..
Manchester.Manchester.
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unipolar NRZ
unipolar RZ
bipolar NRZ
AMI-RZ
Manchester
bipolar RZ
((ISI)ISI)
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((ISI).ISI).
()
ISIISI
sincsinc
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sincsinc
..
() ()
( )H f
1
2s
T
1
2s
T
()
sT sT sT
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:
raised cosine.
2
11 0
2
1 1 1
( ) cos 2 2 2 2
10
2
s
s
s s s
s
fT
T
H f f fT T T
fT
+
= +
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()
1
2s
T
1
2s
T
1
sT
1
sT
( )H f
f
()
.
,
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A/D
( )TH f
( )CH f
( )RH f
A
B
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(ASK, Amplitude Shift Keying).
(FSK, Frequency Shift Keying).
(PSK, Phase Shift Keying).
: Amplitude Shift Keying (ASK),Frequency Shift Keying (FSK) Phase Shift Keying (PSK)
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Frequency Shift Keying (FSK), Phase Shift Keying (PSK).
ASK: => 1, => 0.
FSK: freq. fc-k=> 0, freq. fc+k=> 1.
(BFSK)
FSK .
( )s t
A ft for binary
for binary( )
cos ,
,=
2 1
0 0
( )( )( )( )
s tA f k t for binary
A f k t for binary( )
cos ,
cos ,=
+
2 1
2 0
BPSK: => 1,
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=> 0.
PSK .
PSK: 1 => , 0 => .
( )
( )s t
A ft for binary
A ft for binary( )
cos ,
cos ,=
+
2 1
2 0
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ASK
BFSK BPSK
8-level QAM
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