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 Hp, we can draw the figure of Rp ,and from this figure ,
Trang 1Chapter 1
\ 1-1 \ cl,+d~ =\{iCIDO) +V'llaOO} ~ §4.ILfJt1',f'(J"
d,= f;J;; = i :l,(r ODD) ~ oil- ~ (2 ~"1 E.\"f I., ~ ~ ')
d,+~'1.-= SS~·"e.s ~ PCIl>OO) i- V'J,.~~ -:: S51tt,/es
~ h 1 = (56 - r- ('l»b»~ ::: S 2 H+
'1 1 ."
( htr e ) = d t t"e
:J h7., p hre = d"'J- kJ~~'{' 1, ~< re
~d~2ht'~ ~hd re.:t('J~DIli,k;): 5"2.BDM,7es
Ld· J ::: cnde-"4 At'-ltkf l:r fe.l) atvl d ti, ";,{(S
~ J2 (lIIlles)~ 2,,1, ~;;~ (.s-ll3()N~/e.r)
~cr- -= 1.~ or .d = Vff:
2 d =- :; 0 ni.J~ = 2 {2h =; t[- (1 It): (& ())2
~ I-.-=- (3o)YB = =-~o:::oo!.oIl_ 112
1 1 -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
1 1 -6 11M;}-=: f-i.o,(10)I,D,lf.o1 i.::/} '1-; P':fi:O.lj 1j.=flf~o.1
~ :t~.I - -J" (O.l) _ 2 31" L~ 7:;"';J, -I (o.J) -/7'17':4.
-;r • ~ - J ~ 2 _ I- • (r ) -'4.L.Jf- I~ L - " ·/u
fl :: ~ Pj Ij = 2 ~.l}(l.1u} +{o j} I '73?] :; I C??/6;h
J-
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm Systems 8th Edition, L W Couch, II
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https://getbooksolutions.com/download/solutions-manual-digital-analog-communication-systems-8th-edition-answer-and-script/
Trang 2LET 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
:= 1
h
k
-1
: = -
In(2)
2
k
o
k
From the above figure, we know the maximum entropy is 1 where the
probability for sending 1 or 0 is 0.5
Trang 3P I ::- o.L5 ~l :: ~~ ~ 0,15
o L 5" + 2 (O./S-) -I- cD (a 0)) = 0 •cr I
: ~ ::: t).os ~;""te 2.
/0
p == ',0
H = ' - , 2 p J ~~ ~ (t\ ) ) ~ [~J 11 2 p, J ~ f· j
j - t:Ao'L ";'::'1
=[i-I"L] [ L 5 Lv , ? <; + L l ) , ,,, fr- ,/S
+(<0) ,oi t., ,Of + o~ Jr ,o"l, ]
H ::: S,0 g 4- b,'+~
I 1-11 ~ ,) ?, = 0, ~ • P?:: 0 , '7
(h,) f! IIW>.x (oJ- P; = ~ = ~ = 0 S i ~ I, 1M
II oM'" j =- - L ( 6.5) J,., 6," " 1 b,,' f
"fI""c.'f-b"L
1 1-12 I M ~ /0 ~, :: -L '=: l lo
H = - I() ( J) ~ I =- ~ ~ (2 h ; ts
)ML
f! 3 lA.; +~ 1st c
3
H =
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm Systems 8th Edition, L W Couch, II
Trang 4U ~ 1J I,,~
-/'71
=- f2"[ Ii} I] /11 (1)'1 -/- 3(t/'jyl 3(1)/1]
- 1¥1l
C~ecJ; t' P: ~ l'l[ U/~ J{i.F~
=9 J-J:: 1/ B II> M s oJ"l i '=- 2 U ( ti( tJ'~:: / 0
1 14
(sIAlMB 3
c = I:I>~ l~ [lDllQ - 1 ; 'l'1~ Ii)~
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
SNRdB := 20 dB
SNRdB
10
SNR :;:;:: 10 ==;~===> SNR = 100 (Absolute power ratio)
C := B [log (1 + SNR)] ==> C = 2.131·10 4 Channel capacity (bits/sec)
log(2)
C :::::: = = = > C = 3.044 10 Channel capacity (chars/sec)
b
1
P := - - - - - Probability of each character
chars
log[~]
1 ; = - =========> I = 6.781 bits 109(2)
4
Trang 51 1-16 I R ( S ) [()~ 1-' (I + J D ~o/I~ )
: EI ~ I t i1 :: 'B J ,,~ / t1.) :: 'B ~ Jt, 'l4 q)
(a) ~ J:Lt)O-3DlY~ crbD ~ R '::.(qOQ) (t4l/i/f) :: 13.1-5 k~/fJ"fr
(c) :B-=- 32 DO'" jDe>=' 2'tbTJ ~ ~~ (;l9~ (I'f 9'f-Jl)=- ~3 35 ~ki!J.!r
- Ur\c.oJ~J Jt4+o 1~
l!ti,ff' ,~ 1 b~-h ~t
(S~/ff
()lfi-" -h ~) .,. L -,~-r .L, J.;, L.-r-l
~ ~',Is 4t (, 1i;"e.)
]r, f sf,,(j Y(3,rrey
1-18
x .- 1 x .- 0 x - 1 x .- 1 x .- 1
ga - 1 ga .- 0 ga .- 0 ga .- 1 Gain vector, mod2
gb .- 1 gb .- 1 gb .- 1 gb .- 1
k := 0 length(ga) - 2
v : = 0 k : = 0 length (x) - 1 v : = X
k := length (x) + length (ga) - 1 length{x) + 2 length (ga) - 3
v := 0 i := 0 length (v)
-sa
i
i ~ length(gb)-j-l j+i
j
s := sa s := sb
2 i i 2 i+1 i
sb
i
i := 0 2 length (x) - 1
out := S
i i
For
====>
xT = (I 0 outT = (1
1
1
1
0
1)
1 1 0 0 I l l )
5
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm Systems 8th Edition, L W Couch, II