Chapter 1
\ 1-1 \
cl,+d~
=\{iCIDO)
+V’llaOO}
~
§4.ILfJt1′,f'(J”
‘1.
1..
.”
(
htr
e ) =d t
t”e
:J
h7.,
p
.hre
=
d”‘J-
kJ~~'{‘
1,
~<.
re
2.
d
=-
:;
0
ni.J~
=.
2{2h
=;
t[-
(1
It):
(&
())2..
~
I-.-=-
(3o)YB =.
112.
–=-~o:::oo!.oIl_
11–5
la
:::th
=12
~DO)
=N.I’!”,
,(2..”
:J.
4
…
h
[‘1-)
::
1.83
“‘I’/~
I
Tt1i’al
t’C4.d/~
t>f
cove”4g.~:::J,+~,,=’I¥-‘It/.+,..93::
t’.97IHj 1
es
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II
LET
p–The
probability
for
sending
a
binary
1,
then
the
probability
for
sending
a
binary
0
is
(l-p).
From
the
entropy
formula
for
H(p),
we
can
draw
the
figure
of
R(p)
,and
from
this
figure
,
we
can
find
the
maximum
entropy
and
the
p.
R(p)=(p*ln(P)+(1-p)*ln(1-p»j(-ln(2»
k
:=
0
••
50
P
k
:=
k
–
50
HMAX
:=
1
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II
P
I
::-
o.L5
.
~l..::
~~
~
0,15
.
·\1-10
) )
f‘f =
~
5
“-
P
~
:.?)
“P
g
=-
PC[
=
D,
0 /
I
1-11
~
,)
?,
=
0,
~
•
P?::
0 ,
‘7
D,3bo.s
+O,(~O,I
_~
L
b”L
1 1–
12
IM
~
/0
~,
::
-L
‘=:.. l
lo
) 10
.)
t
H = – I
()
(.
J)
~
. I
=-
~
.
~
(2.. h ;
ts
)ML
3
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II
1
1
13
–
I,~
LI~;r
.,(11;-&
/w…I
1>1=2.’1-
)
~
=~);r
~
~
i
e,,~fl
j=t
Jt
1
14
1 –I B
-”
3~o
U-z
t~
)”8
“3tlJ B
c=
~
Jp~l.[l-l~)]
~
/;1.
/11
[if
~
j *
~)J8/b
I.,j-fr)
1-15
1
(a)
chars
:=
110
Number
of
characters
available
log
(
chars)
]
b
:=
ceil
Number
of
bits
required
to
represent
a
character
[
log(2)
====>
b = 7
bits
(b)
B:=
3200
Hz
Channel
bandwidth
SNRdB
:=
20
dB
Signal
to
noise
ratio
b
(c) Assuming
equally
likely
characters,
information
content
of
each
character
is:
4
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II
1 1–
16
I R
(S
)
[()~
1-‘
(I
+J D
~o/I~
)
:.
EI
~
I t
i1
::.
‘B
J
,,~
/.
t1.)
::
‘B
~
Jt,
‘l4
q)
[i
-17
=-J
~
t;
~
sL;ff.
re1lsto-
–
Ur\c.oJ~J
Jt4+o.
1~
l!ti,ff’
,~
1
b~-h
~t
“
-h
~)
…….,.–L..-,~-r–.L,–J.;,–L.-r-l
1-18
x
.-
1 x
.-
0 x
.-
1 x .- 1 x
.-
1
Input
vector
0123 4
ga
.-
1
ga
.–0
ga
.-
0
ga
.- 1
Gain
vector,
mod2
adder
01 23
gb
.-
1
gb
.-
1
gb
.-
1
gb
.-
1
Gain
vector,
mod2
adder
0 1 23
sa
i
sb
v
:=
V
[9b
]
i
~
length(gb)-j-l
j+i
j
s
:=
sa
s
:=
sb
2 i i 2
i+1
i
sb
i
5
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II