ECE- 4603 http: //w w w . csc. gatech. edu/~copel and/4603 Pr - - PDF document

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ECE- 4603 http: //w w w . csc. gatech. edu/~copel and/4603 Pr - - PDF document

Oct 05, 2023 363 likes •434 views

ECE- 4603 http: //w w w . csc. gatech. edu/~copel and/4603 Pr of . John A . Copel and j ohn. copel and@ ece. gatech. edu 404 894- 5177 O f f i ce: GCA TT 579 em ai l or cal l M r s. KathyCheek, 4- 5696, f or

slide-1
SLIDE 1

ECE- 4603

http: //w w w . csc. gatech. edu/~copel and/4603

Pr

  • f

. John A . Copel and j

  • hn.

copel and@ ece. gatech. edu 404 894- 5177

O f f i ce: GCA TT 579 em ai l

  • r

cal l M r s. KathyCheek, 4- 5696, f

  • r
  • f

f i ce vi si t ti m e Suppl em ent to Chapter s 3 and 5

Data & Com puter Com m . , p 95- 98, 148- 155

  • A nal
  • g

to Di gi tal Conver si

  • n
  • Bandw i

dth ver sus Capaci ty

  • Nyqui

st and Shannon equati

  • ns.
  • Si

gnal Degr adati

  • n
  • Basebase

and Br

  • adband

Encodi ng

ECE4603 5a

A nal

  • g

and Di gi tal Si gnal s

A nal

  • g

Si gnal

  • val

ue var i es conti nuousl y

  • Sound
  • ai

r pr essur e w ave, can be conver ted to anal

  • g

vol tage

  • r

cur r ent w ave by m i cr

  • phone.
  • El

ectr i cal (anal

  • g)

voi ce f r equency si gnal s

  • can

be conver ted to sound by l

  • udspeaker

.

  • Pi

ctur e

  • l

i ght (col

  • r

, br i ghtness) var i es conti nuousl y w i th posi ti

  • n.

Di gi tal Si gnal s

  • str

i ngs

  • f

di scr ete val ues w hi ch can be r epr esented by bi nar y num ber s, str i ngs

  • f
  • ne'

s and zer

  • s.
  • Ti

m e- var yi ng anal

  • g

si gnal s ar e conver ted by aver agi ng the val ue

  • ver

a ti m e i ncr em ent and assi gni ng a bi nar y val ue.

  • I

m ages ar e di vi ded i nto sm al l ar eas (pi xel s), then col

  • r

and br i ghtness ar e aver aged

  • ver

each pi xel and tr ansm i tted ar e stor ed i n di gi tal m em or y sequenti al l y.

Conver si

  • n
  • f

A nal

  • g

to Di gi tal

Ti m e i ncr em ents, dt, m ust be sm al l enough to captur e hi ghest- f r equency com ponents

  • f

i nter est. The num ber

  • f

A m pl i tude I ncr em ents, n, m ust enough to gi ve an adequatel y- accur ate esti m ati

  • n
  • f

the anal

  • g

si gnal . The bi t r ate i s n/dt (bi ts per second). 7 = 0111

  • 7

= 1111 = 0000

1101 =

  • 5

0101 0101 0101 1101 1101 1101 Bi t Str eam Reconstr ucti

  • n

Reconstr ucti

  • n

af ter l

  • w -

pass f i l t er 4 bi ts

  • >

16 l evel s m axi m um

Sam pl i ng ti m e = dt

bi nar y num ber s f

  • r

aver age val ue

  • f

si gnal dur i ng dt i nter val s 0101 = +5

slide-2
SLIDE 2

Di gi tal V oi ce

  • V oi

ce i s r ecogni zabl e and i ntel l i gi bl e w hen f r equency r ange i s l i m i ted to 300 to 3400 Hz (Her tz = cycl es/second) and quanti zati

  • n

noi se <

  • 20

dB.

  • Tel

ephone standar d i s to di gi ti ze 8000 ti m es per second (dt=125 m s) and to use 128 l evel s (8 bi ts i ncl udi ng si gn).

  • Thi

s r esul ts i n a bi t r ate f

  • r

a voi ce channel

  • f

64, 000 b/s.

Di gi tal M usi c

  • M usi

c r equi r es a f r equency r ange up to 18, 000 Hz and quanti zati

  • n

noi se <

  • 65

dB.

  • CD

m usi c i s di gi ti zed 44, 100 ti m es per second (dt=23 µs) i nto 32, 000 l evel s (16 bi ts i ncl udi ng si gn).

  • Thi

s r esul ts i n a bi t r ate f

  • r

a CD m usi c channel

  • f

710, 000 b/s (ti m es 2 f

  • r

ster eo). Tel ephone V oi ce (Sound W aves) M odem A /D Channel Bank Di gi t al Tr unk 64 kb/s I SDN Tel ephone V oi ce (Sound W aves) I SDN Sw i tch Di gi t al Tr unk 64 kb/s PC Anal

  • g

Sw i tch

0110010101100110

A nal

  • g

and Di gi tal Si gnal s

RS- 232 28, 800 kb/s 64, 000 kb/s 01100 01100 01100 01100

Channel Bandw i dth ver sus Capaci ty

  • Capaci

ty = Rate i n bi ts/second (b/s) that bi ts can be tr ansm i tted.

  • Bandw i

dth = Fr equency r ange (w i dth)of the channel (Her tz).

  • M axi

m um Baud Rate (sym bol s/sec), B = 2 H

  • Noi

se = Unpr edi ctabl e devi ati

  • n
  • f

r ecei ved val ue due to al l causes (pr

  • babi

l i ty bounded by acceptabl e er r

  • r

r ate).

  • Ther

m al noi se, Cr

  • sstal

k, I m pul se, I nter m odul ati

  • n,

. . .

  • Nyqui

st Theor em f

  • r

a noi sel ess channel : gi ven a bandw i dth H and a si gnal w i th L di f f er ent l evel s, the capaci ty C i s gi ven by: M axi m um Data Rate (bi ts/sec), C = 2 H l

  • g

2(

L )

  • Shannon'

s Theor em f

  • r

a noi sy channel w i th si gnal to noi se r ati

  • S/N

i s gi ven by: C = H l

  • g 2(

1+S/N )

slide-3
SLIDE 3

M axi m um Sym bol s ( Baud) per Second

1 1/R 1/2f

Si nce Bandw i dth (H) = f m ax: Rm ax = 2 f m ax =2 H The m axi m um num ber

  • f

i ndependent ti m e i nter val s (sym bol s) i s equal to tw i ce the bandw i dth.

Num ber

  • f

Bi ts per Sym bol

10 00

The num ber

  • f

bi ts per l evel , N bL, i s l

  • g 2(L).

Level s Bi ts 2 1 4 2 8 3 16 4 32 5 64 6

Tw o bi ts per sym bol r equi r es 4 l evel s.

11 01 10 11 01 00 01 1 1 1 1 1 1 1 1 1 1 1 1 1 01 1

Thi nk

  • f

a "Baud" as a "Bucket" that hol ds a cer tai n num ber

  • f

bi ts. The num ber

  • f

bi ts per second that pass a cer tai n poi nt (or ar r i ve at a node) = the num ber

  • f

Baud (Buckets) per second m ul ti pl i ed by the num ber

  • f

bi ts car r i ed by each Baud (i n each Bucket).

slide-4
SLIDE 4

The Capaci ty (m axi m um bi t r ate) i s equal to the m axi m um num ber

  • f

sym bol s per second (2 x Bandw i dth) m ul ti pl i ed by the num ber

  • f

bi ts per sym bol { l

  • g2(L)

}.

  • Nyqui

st: C = 2 H l

  • g2(L )

I ntui ti vel y, the m axi m um num ber

  • f

l evel s w i th an m axi m um si gnal vol tage V s i s appr

  • xi

m atel y V s/V n, w her e V n i s the noi se vol tage (separ ati

  • n

vol tage betw een l evel s needed to r educe er r

  • r

s due to noi se to acceptabl e val ue). Cl aude Shannon (f ather

  • f

I nf

  • r

m ati

  • n

theor y) f

  • und

a m or e exact val ue as a f uncti

  • n
  • f

the r ati

  • f

si gnal pow er S to noi se pow er N.

Shannon: C <= 2H l

  • g

2( (S+N)/ N)

<= H l

  • g 2(S/N

+1) to m atch Nyqui st: L <= (S/N +1) = (S+N )/ N L <= (si gnal + noi se vol tage)/(noi se vol tage)

V n L=4 V s=4V n

Pr

  • babi

l i ty

  • f

r ecei ved l evel f

  • r

4 tr ansm i tted l evel s.

Si m pl i f i ed Concept

  • f

Shannon' s Law Si gnal Degr adati

  • n

A l l r eal si gnal s ar e anal

  • g

by natur e. W hi l e the tr ansm i tter m ay send exact di scr ete l evel s i nto a physi cal tr ansm i ssi

  • n

l i ne, the r ecei ver sees a degr aded si gnal and m ust deci de w hi ch di scr ete l evel expected i s cl

  • sest.

1

0. 0v 0. 2v A ttenuati

  • n
  • l
  • st
  • f

str ength (am pl i tude) Bandw i dth cutof f

  • l
  • st
  • f

hi gh- f r equency com ponents.

Data Tr ansm i ssi

  • n

Types

A nal

  • g

Baseband

  • V oi

ce Tel ephone

Di gi tal Baseband

  • I

SDN V oi ce

  • Ether

net

  • PC

Com m Por t Br

  • adband

Baseband Fr equency 50 M Hz 1000 M Hz

A nal

  • g

Br

  • adband
  • A M ,

FM , TV , Cel l ul ar (A M PS)

Di gi tal Br

  • adband
  • Di

r ect- TV (satel l i te)

  • PCS,

Di gi tal Cel l ul ar

  • Di

gi tal CA TV

slide-5
SLIDE 5

Data Encodi ng Schem es

Baseband

  • f

r equency r ange i s f r

  • m

Hz to f

m ax

(B = fm ax) Br

  • adband
  • f

r equency r ange i s f r

  • m

f m i

n

to fm ax (B = fm ax

  • fm i

n)

W i th br

  • adband

si gnal s, data i s m odul ated

  • nto

a car r i er w ave w hose f r equency i s at the center

  • f

the band. Com m on types

  • f

m odul ati

  • n

ar e:

  • A m pl

i tude Shi f t Keyi ng (A SK)

  • Fr

equency Shi f t Keyi ng (FSK)

  • Phase

Shi f t Keyi ng (PSK)

  • Q uadr

atur e Phase Shi f t Keyi ng (Q PSK)

  • Q uadr

atur e A m pl i tude M odul ati

  • n

(Q A M )

W i th al l com m onl y- used Br

  • adband

m odul ati

  • n

schem es: Bandw i dth (Hz) = Baud Rate (Baud/second)

Br

  • adband

M odul ati

  • n

Encodi ng

A si ne w ave w i th ar bi tr ar y am pl i tude A and phase ø can be r epr esented by the am pl i tude

  • f

the i n- phase and quadr atur e com ponents, P & Q : V (t) = A si ne(w t+ø) = P si ne(w t) + Q si ne(w t+90)

P Q P Q P Q P Q

Q PSK 2 bi ts Q A M 4 bi ts PSK 1 bi t A SK 1 bi t

Each state i s r epr esented by a dot i n the "constel l ati

  • n"

di agr am .

Baseband Encodi ng Schem es

Pr

  • bl

em s to

  • ver

com e

  • Tr

ansi ti

  • ns

needed to synchr

  • ni

ze r ecei ver bi t cl

  • ck
  • DC

r ef er ence l evel needs to be m ai ntai ned

1 1 1

RZ

  • Retur

n to Zer

  • NRZ
  • Non

RTZ

Good r ef . , doubl es bandw i dth Tr ansi ti

  • ns

not cer tai n

NRZ- I I nver ted

Di f f er enti al : Pol ar i ty i nsensi ti ve

M an- chester

Good ti m i ng, doubl es bandw i dth 30

Bi t str eam