Solutions Manual Digital & Analog Communication Systems (8th Edition) This is completed solutions manual for Digital and Analog Communication Systems 8th Editor.Edition (United States), by Leon W. Couch, II, Pearson/Prentice Hall, Upper Saddle River, NJ, 2011. This Solutions Manual for Digital and Analog Communication Systems, 8th Edition (United States) contains complete solutions for the homework problems in the 8th Edition. If the problem is designed for a MATLAB or MATHCAD computer solution, then the MATHCAD printed solution is shown. (MATHCAD solutions are shown since they clearly display the algorithms used and the output takes up less space.) Click here to view Example: (Chapter 1) : Solutions-Manual-Digital-&-Analog-Communication-Systems-8-editor Example

1. Chapter 1
1-1 cl,+d~ ={iCIDO) +V'llaOO} ~ §4.ILfJt1',f'(J"
[ 1-2 J U.rin, (1-/), d. ~
d,=f;J;; =i:l,(rODD) ~ oil-~ (2..~"1. E."f I., ~ . ~').
d,+~'1.-= SS~·"e.s ~ PCIl>OO) i- V'J,.~~ -::. S51tt,/es
~ h1 =(56 - .r-('l»b»~ ::: S2. H+
'1. 1.. ."
( htre ) =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[- (1It): (&())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'.97IHj1es
1 1-6 11M;}-=: f-i.o,(10)I,D,lf.o1 i.::/} '1-; P':fi:O.lj 1j.=flf~o.1
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fl ::..~ Pj Ij =2. ~.l}(l.1u} +{o. j}I. '73?] :; I.. C??/6;h
J-.
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~ I Ip<jJl} ~ JD~('f} "9 1= :~:r.f =- ID~1. (K)
1
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II

2. 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
h
k
-1
: = - ­
In(2)
2
h ,HMAX I------+-----:=--+----=====--+------i
k
o
o P 1
k
From the .above figure, we know the maximum entropy is 1 where the
probability for sending 1 or 0 is 0.5.
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II

3. PI
::- o.L5 . ~l..:: ~~ ~ 0,15 .·1-10 ) )
f'f = ~5 "- P~ :.?) "Pg =- PC[ = D, 0 /
o. L5" + 2 (O./S-) -I- cD (a. 0)) = 0 •cr I
:. ~ :::. t).os ~;""te 2.
/0
p. == ',0'0 ~j ~ I
~ to
H= 2 p. ~~ ~ (t ~ [~J 2 p, ~ f·'-, J .)) 11 J j
j- ..t:Ao'L ";'::'1
=[i-I"L][.L5 .Lv. ,?.<; + Ll ) , ,,,. fr- ,/S­
+(<0) ,oi t.,.. ,Of + .o~ Jr. ,o"l, ]
H ::: S, 0 g 4- b,'+~
I1-11 ~,) ?, = 0, ~ • P?:: 0 ,'7
D,3bo.s +O,(~O,I
_~ L
o. gg I bl'ts
(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
) 10 .) t
H = - I() (. J) ~ . I =- ~ . ~ (2.. h;ts
)ML
T~ li- :: S,5LL ~;+~ :; /,11 Sft, ::.T
f!... 3 lA.;+~ 1st.c.
3
H =
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II

4. 11 13
- I,~ LI~;r .,(11;-&/w...I 1>1=2.'1- ) ~=~);r~ ~i e,,~flj=tJt
U.. ~ 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/. BII> Ms oJ"l i '=- 2. U ( ti(tJ'~:: /. 0
1 141 - I B -"3~o U-z t~)"8 "3tlJB
c= ~ Jp~l.[l-l~)] ~ /;1. /11 [if ~j *~)J8/bI.,j-fr)
(sIAlMB 3
-q- iJ:: ID J~ :::. (D':: II> Db
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 Channel bandwidth
SNRdB := 20 dB Signal to noise ratio
SNRdB
10
SNR :;:;:: 10 ==;~===> SNR = 100 (Absolute power ratio)
C := B. [log (1 + SNR)]
4
==> C = 2.131·10 Channel capacity (bits/sec)
log(2)
C 3
C :::::: ­ ===> C = 3.044 10 Channel capacity (chars/sec)
b
(c) Assuming equally likely characters,
information content of each character is:
1
P := ----- Probability of each character
chars
log[~]
1 ; = - ­ =========> I = 6.781 bits
109(2)
4
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II

5. 1 1-16 I R (S ) [()~1-' (I + JD~o/I~)
:. EI~ I t i1 ::. 'B J,,~/. t1.) :: 'B ~Jt,'l4q)
(a) ~ J:Lt)O-3DlY~ crbD ~ R'::.(qOQ)(t4l/i/f) :: 13.1-5k~/fJ"fr
(6] B::. 31t)~ -U;on-='/7oo:1 R:::.V7tJ~(j~91-q) '= 7-5~ 'H kl;cfs!r
(c) :B-=- 32. DO'" jDe>=' 2'tbTJ ~ ~~ (;l9~ (I'f.9'f-Jl)=-~3. 35~ki!J.!r
[i-17=-J ~ t; ~ sL;ff. re1lsto­
- Urc.oJ~J Jt4+o. 1~
l!ti,ff' ,~ 1 b~-h ~t
(S~/ff ()lfi-
"-h~) .......,.--L..-,~-r--.L,--J.;,--L.-r-l
COd~J :l~t~ o~t
. . ~ ~',Is 4t(,. 1i;"e.)]r,f sf,,(j Y(3,rrey1-18
x .- 1 x .- 0 x .- 1 x .- 1 x .- 1 Input vector
0 1 2 3 4
ga .- 1 ga .- 0 ga .- 0 ga .- 1 Gain vector, mod2 adder
0 1 2 3
gb .- 1 gb .- 1 gb .- 1 gb .- 1 Gain vector, mod2 adder
0 1 2 3
k := 0 .. length(ga) - 2
v : = 0 k: = 0 .. length (x) - 1 v : = X
k k+length(ga)-l k
k := length (x) + length (ga) - 1 .. length{x) + 2 length (ga) - 3
v := 0 i := 0 .. length (v) - length (ga)
k j := 0 .. length (ga) - 1
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
i := 0 .. 2 length (x) - 1
out := S
i i
For
====>
x T = (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