• Author / Uploaded
• Sydney

Citation preview

INSTRUCTOR SOLUTIONS MANUAL (United States Edition)

Digital & Analog Comm. Systems 8th Edition, L. W. Couch, II

Chapter 1 \ 1-1

[ 1-2

cl,+d~ =\{iCIDO) +V'llaOO} ~ §4.ILfJt1',f'(J"

\

J U.rin,

~ E.\"f I., ~ . ~ ').

(1-/),

d.

=i :l,(r ODD) ~ oil-~ (2.. ~"1.

d,= f;J;;

d,+~'1.-= SS~·"e.s

~ PCIl>OO) i- V'J,.~~

.r- ('l»b»~

~ h1 =(56 -

=d

'1.

(

htre )

1..

S 2. H+

:::

t t"e

-::. S51tt,/es

."

:J h7.,p .hre = d"'J- kJ~~'{' 1, ~ Db

c=

2. U ( ti(tJ'~::

/. 0

*~)J8/b I.,j-fr)

:::.

c.. =I:I>~ l~ [lDllQ 1-15

- 1. 'l'1~ Ii)~ ;

1

chars := 110

(a)

b := ceil

Number of characters available

log (chars) ] [

Number of bits required to represent a character

log(2)

====>

b = 7

B:= 3200 Hz 20 dB

Channel bandwidth

Signal to noise ratio

(b)

SNRdB :=

bits

SNRdB

SNR :;:;:: C := B.

10

10 ==;~===>

SNR =

100 (Absolute power ratio) 4

[log (1 + SNR)] log(2)

==> C = 2.131·10

===>

C = 3.044 10

C

Channel capacity (bits/sec) 3

C :::::: ­

Channel capacity (chars/sec)

b

(c) Assuming equally likely characters,

information content of each character is:

1

P

:= - - - - -

chars

Probability of each character

log[~]

1;=-­

109(2)

=========>

I

4

= 6.781

bits

INSTRUCTOR SOLUTIONS MANUAL (United States Edition) 1

1 -16

I

R

:. EI~

Digital & Analog Comm. Systems 8th Edition, L. W. Couch, II

[()~ 1-' (I + J D~o/I~ )

(S )

J ,,~ /. t1.)

i1 ::. 'B

It

(a) ~ J:Lt)O-3DlY~ crbD ~

::

'B ~Jt,'l4 q)

R'::.(qOQ) (t4l/i/f) :: 13.1-5 k~/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 Ur\c.oJ~J Jt4+o. 1~

~ t; ~

sL;ff. re1lsto­

l!ti,ff' ,~ 1 b~-h ~t "-h ~) .......,.--L..-,~-r--.L,--J.;,--L.-r-l

COd~J :l~t~ o~t

]r, f

1-18 .-

x

.-

x

1

0

1

ga

.0

.-

gb

1

2 1

k

:= 0 := 0

v

0

.-

gb

1

.- 1 ga .- 1 3

gb .- 1

x

1

2

.

x 4

3

.-

ga

0

.-

gb

1

0

.- 1 2

.-

ga

1

x

0

.

sf,,(j Y(3,rrey

.-

(S~/ff

1

()lfi-

~ ~',Is

Input vector

Gain vector, mod2 adder

Gain vector, mod2 adder

3

.. length(ga) - 2 k : = 0 .. length (x)

-

1

:= X

v

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

k

sa i sb

:=

i

V

~

[9b length(gb)-j-l

v

]

j+i

j

sb

s i

i

:=

out

0 .. 2 length (x)

:=

i

- 1

S

i

For

s

sa

:=

2 i

i

xT

=

(I

====> out T =

0 (1

1 1

1 0

1) 1

1

0

0

Ill)

5

:=

2 i+1

sb i

4t (,. 1i;"e.)