Principles of Communication Systems SVIT 18EC53

MODULE-4: SAMPLINNG
&
QUANTIZATIONN
4 1 INTRODUCTlON:

8yglem, botk are sed to trangmiYt

Digita) s well B Analog
-

bignas fom Dne place fo ano

Her
he t r a k n i s s i o n ot fnformati i done
Communi@tion
a
Analog
J
nanalog form. [ontiouous signa)
Conttauous signas, vepTesenkd
Analog Bignak ase

Sne waves
ConHnuous
Ex: Human Voice, Natuagl So uad anga
Digital Communiouhon thetraas mission f mformd hôn
oone n Digila form.[ Díscrel signa ToJe L1|
Digita Signak are, Discoeti 8ignag,TEpreBenRa by
S u a e wave
has Disconhnuous
Compujexs, opHcal dai ver
alues
The eppect of Distootien, Noise and Ink»fesence is much Jess
o
digital &igna 3 . Discre Circusa ae move Teliabk, eaty
deßign ad cheafes lhan analog ciscui
The F? TSE stp m digital Cemmuniafion &ystam î_ he Converien

analog 6iqnal b a Digfta o?8cetaRme ignal.

|A
|Analog
SAMPLIN 6 QUANTIZATION ENcODING
6lo lo lo
TUU
Digita
ignas FeSteps Analog la pigitaCowersionn Signa
The Key 8 t p s nvolved m he Convession ot ftnalog signal t

Digital Signal a r 4.SAMPLING

2.UANTIZATION
3. ENCODI NG
The complete delails Sampling Quanhzatentechniques, Entoding
TehnigUe3 are_presenkd m this Module and Cestnued fn Medule-5
Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT venkatesha.m@saividya.ac.in
Principles of Communication Systems SVIT 18EC53
=

. Why digitize Analog Sources VTUMODEL RP*

ave:
DIGITAL SIGNALLS Dver ANALOGG
The advantagez of U8ing
he eprec of Distortion, Noise and Iotev fexence much
less n digital ignal
DBcrek cîrcui ase mose elable, egier o design & cheapey
than a0alog Ciscui
3 i ligita) Kysems, 1t k egier b tn*q7e dYPPeen
Services.
Ex: Video +Soundtrack
e t e r1 0

4 Digtal signalg are sampler 5 characeri3e and tyPICa

Go not have tke Same anpiude Tange and vasidbility
Analog Bignalg.
. Digital circuig ase ess Serl tve to physical ePpeg such
a3 Vibraien & Emperature.
6
Digfta) 8 skmg ase ess SeniH ve b Nolse tha) analog
7. The tTasmission Scheame TS Telatively îndependent of he

ousce
8. Mulhpexing trchniques, ase moe eoily împlemen ed sitf
drgftalbasmisSion Stoalease.
9. There asetchniques For semoving Tedundancy | Addng-
edundancy to ad97laltranamission. Such lhat the euos
TFat Occud dusing-trasmission may be Corecd at ie
eciever
lo. High Secuit
I. Tn Dii tal &ysems he eTor owechion Dekcian ehnig-
-ues Can be mplem ened easly.
Techniues Such 8 EqUALIZATION, eSpetialy Adaptive Ved5ien3,a3e Easier.
Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT venkatesha.m@saividya.ac.in
Principles of Communication SystemsS SVIT 18EC53 3
=

4 d1 COMPARISON BETWEEN ANALO G & DIG TAL CM¥IUNICATION

W

PARA ME TE R ANALO G DI6 TAL

Ys TEM
TAAALZALAVAALA
SysTE
Tmmunity to NoIsE LESS MORE

. System Complexit MOREE LESS

TMplemenkahon
3. Systm Cos+ MORE
LESS

4. ErTos Detetion
& Not possi ble possible
COrecHon
5. TnfoT rna Hon less High
Seustt (suitable Fr
Military appiahons)
6 MuHpRxin
FDM
Technigue used TDM1

7. Bandwidth Requikme Less xDue o higher

n
bt raes, highez
Channel Bandwidt5
is Tequired.
I t is not possi ble l6
8. REpEATE RS age separai NoISE &
|REPEATERS Can be
|S|ANAL. 75er* pot sed.
REPEATERS Cannot be|
sed.

|9 ProTammingCocina. Not possi ble possi ble.

10 Modulation Techniues. AM,FM, phase-Mad. ASK FSK. PSK<

PPM pWM PAM
I1. SyNCHRoNIZATI ON not De Guire d
reircd
12.
ualty f REcoN STRUCTON C0OD . E xcellent
Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT
venkatesha.m@saividya.ac.inn
Principles of Communication Systems SVIT 18EC53 4
43 SAMPLING PROCESS
VTU MODE L ®P
Stat SAmPLIN6-THEORE M and explain the same wi
Sketches and equation8. 7Mars

SHalemen: SAMPLING THEDRE M, States tiat Any Coninu oLA time

i5 Sampes
base band Signa) can be completely ve preSenkd by
and Tecovesed from i Sampks ¥ he Sanplingt Preguegc
s Greaker han o equa to twice The highegtre9uenu present|
n he bose band Bigna
e., SamplingFaequeny

Whese,
Where, W= Maximun frequeny pveaend in base band 54
Max( ( ns tn, ng .-)
pToof-
Consider an orbitrany fgna xt).4 4nik energ,.
which s Spedfied for all fme ins-anl.

A seament ot he Signa zt) 6

shown n Figue 1a)

L e r S(t) represenR he pesiodic mpulse train and

6iven by Sct)= 2 St-nt), showa hm Figue.
nE-00

whese , tekez all possi ble Valuez of integers.

TsSamplng period =

TFe vecdpovcao Sampng period CT) ts Called sam plng

Ta ,f
L The ananeous Sampling of siqna xtt) is mdioed
n Figur 1¢).

Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT

venkatesha.m@saividya.ac.in
Principles of Communication Systems SVIT 18EC53 3

Xt)

Figu 1 (a); Analog

PoThion of X(4) sI

St )
FiguR.1(b):
Tbahn Impulses
3 23 31s 4 5Ts 6T 1
T,
gt)
Figu1C) Discoe/
Sdmpled signa Sanpled
nal.
Ts 2Ts 3Ts

|L Let ( t ) denotes the signal obtained by Muiplying

a(t) ot evey s second
ScA) and stantaoeous Value of
7he Sanped Aignal: ct) t8 given by,
zct)= «(ct). Sgt

t)= gt)
St)= S(tnTs)

Dr. Venkatesha M, Associate Professor, Department of ECE, sVIT venkatesha.m@saividya.ac.in

Principles of Communication Systems SVIT 18EC53 6

substituli S4) 2 St-nT, Toain f Inpulse

n- o

t)= z t). S(-nTs)= 2ztt).S(t-E)

0-00 n3-00

using Bhi Pting pvoper h tanpuee funchon

W.K. T.
Xt).8(t-nTs)= Z(nTs). S (t-n+s)
Sampled
sct)= -00
(nT).S(t-nT) vedsion o X(¢

(3)
Ia Fre uency dormai),
Coside, t ) = C). SCE)
Taking Fourier tras-fosm n bothsides We get
Muliplicahn
hme Domaio is eta
xCF) = x(P)*S,CP) to CONVOLUTION (*)
>(4) to FoeUeny
domain
Whese,
S 4)=f. Z S(f-nfs)
Usna tn (4).

sCF)= xCP) * fsz n-0

s(f-nfs)

sC*)= fsx(F) *Z S(P-nfs)}

Foem ConvoluHon pppesty f iompue funtien,
WK.T xP)* S (P- nfs)= X(f- nfs)
.'6) g F) =
Psi 0-DoxCF)* &Cf-nFs)

x(F) Fs (F-nfs)(
Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT venkatesha.m@saividya.ac.in
Principles of Communication Systems SVIT 18EC53
EUation (7) Can be Te- WsiHeo

) = fs X(F) + Fs 2 xCf-nfs)
When e
&petrum XGP) 15 passed though an LP
tBen he Second esm n RHS o equaion(e) is elinioa td
Tesu m,
gCF)= Fs XF)
Band lm:}ed.
x (P) =X") ) ziqnad & be
RECOVE RED fon
Whese f.=aH= 3 [Max (im,fns, )) Sampled versim"

A XCP)
Xo)

-P
(a)
XsCR)

fsaw (
ig ) ) Spetno tshidly band n ted Bignal 1t)
(b Spechm f a Sampled version of xt) far T -

Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT

venkatesha.m@saividya.ac.in
Principles of Communication Systems SVIT 18EC53

We map now s l a the Samplna keorem, n two euivalent

Pa
I. A Bage band 8igna of Pini energt, ompelely descabed
Specying e buez of he 8ignal at 8tant me
b
Sepavaid by Ts= L seconds

A band limited Bignal f Finit enes3y, may be Conplel

ecovered foom a knowledge of ig Sampes te Ken at the Tale

op Fsaw" Sampes pes second
NyQUIST RATE
A Sampling qali of Ws ampes pes setond, f r a 89na
bandwsd w'Hext is Called Nyguist *at

Le, Nyquist Ra = aw It B+e mininum Samplig

reueocy deguired.
NyquiST NTERVAL,-
TFe dedpocal of Nyquist Ta is called Nyquist Ioderyal.
is mea3ured m Seconcg

Nyuist Intertal= Seronds

Nyuist a a QW

Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT venkatesha.m@saividya.ac.in

Principles of Communication Systems SVIT 18EC53

4.3.1 TRe Cenceptt of UNDERSAMPLING & OVER SAMPLING

m

when Samplng Preg uene fs=aw. then he tupe

Sampln i4 Called critial FamplingJNyguist ui Senplog.
Resul m No-A liagkng- ejhect& No-GUARDBAND
Xg CP)

N=Ps
M s 2Ps
&1: Nhen fs= aN CNyQoIST RATE)

ii)
Ku Whern
ts &N-[UNDER SAMPLING)
When
fs <aW, jt rezulg fn undeo Sampl9 & Here
i be
aliasing ePpec [oves lapphngJ.The Spetun is Shoun
nFig.2. fathis Coße ft is tmpossi bleto oe coves (he Signd.
RsCF)

Fig2 when fs <aN GAiasig

When s aW:-[oveR sAMpLIN6)
When Ps W, ?t vesulG oer Samplin 8 there will be
Cuard band Hu he adjacent Spehun 2Ct). It is esy To tCovexr
gC) the Siga.
qUARP
BAND

A
:fo Recovytouthionf signa) t ) :Sampling fieuenu f22w
Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT
venkatesha.m@saividya.ac.in
 Principles of Communication Systems SVIT 18EC53 1o
o IMPP
Numeica) Prob lems on NyQUIST RATE &NyQUIST INTERVAL;-

Foulade
Nyyist da =a t ' samples per Second HZ
whest W= Max ( , n , . .)) present n given base band
8ignalxtt).
.Nyguist IokrVal= Secondg
NyUist Tdh W

VTu OLOp
1 Deksnine he Ny9uist rat acd Nyuist fkrval for: JynelJuly
2011
( m(t)=-Sin (50omt)(i) 2t) =Sioca00t)
Tt
Ai m(t):-[sinc5ont))J
a50 HZ =W
w 500N aTf500 >P
Nyuist Tah=QWe a fm500 HZ Sanples|sec

Nyuist Jokaval= setend3

Nyuist daa 500

i> 2(4) = Sinc (At)

HkT Sioc (*) = Sin (Ta)
ct) = Sin c loot=- sin (aont)

200x A7in -00 fm200W= loD Hz

W
' . Nyuis Tat= aw: a f ax10D =a50 H2

Nyuist Joerva| Secomdg

Nyuist Ta 0d

Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT venkatesha.m@saividya.ac.in

Principles of Communication Systems SVIT 18EC53

a A n ana log 6igna) 8 ex pse Ssed by e evuati on

= 3 cos(s0nt)+ 1osin (300nt) +Cos (1607t. calcula

e Nyuist raü and Nyuist Inkrval.
|L Given: R H)= 3Cos (50Tt)+ 10 Sin(3007t)cos((udA*)

Comparing equathion(1) 9 h stonclad equatim

xCt) 3 cos(w,t) +
=
10gig(,t)+cos t )
We 8e

w 507
W30D

5 150 5o
ms

W= Max G Tmn=Max (A5, 150, 5o)

2

= 150 HZ

Nyuist Kat aW= axi50 300 H Samplssa

3:333ms
NyUst Inkrval = .

NyoistTo(3)

Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT venkatesha.m@saividya.ac.in

Principles of Communication Systems SVIT 18EC53 12

KAn analeg gigna) is exp>eszed by the l a ion

)= cos (40Ont)-Cos (1o00ñ)
Calcula the Nyuist a l and Ne9ust Jokrva.
|L Ct)= cos (4000Rt). Cos
(1poont)
Wk-T CoSA CosB = cos(A-B)4 tos (A+E)

t)= COs (300o Tt)+coS(S o00Rt}|

A-B AtB

.rA)=-cos (3000 t) + cos (5oo0x t)

4T 4
D
-(2)
Com pesing iI5 standard euahon, e ge
w>3000T 500
2 5000

1500 m250o

W Mx(tm, n = M-x (50o, 2500)= 2500 Hz

Nyquist Ra 2W= K5u7 =5000o Hz O Sanplesse

Nyuist Ioterval= = 0-amS

Nyuist Ra 5000

Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT venkatesha.m@saividya.ac.in

Principles of Communication Systems SVIT 18EC53 13

44PULSE AMPLITUDE MDDULATION **

VTUMODEL QP
PAM)
FLAT Top SA MPLIN6.
Explaim the generation and vecovemy pAMCFlat-To p) Signa)
Ji necess qy equations and 8pechum didqram

Definihon- T+ 1s an-Analog pulke Madulahion Scheme n which

te ampliudes a train o Tecangular Carnier

Pul ses ase Varied n acoTdance wik the sqmple
Values modulatina aigna.
I n PAM, the top op each mnodulake d vectengu laa pul ses
maintained f lat. Heno pulseAapli tucle Modulaim CPA M)
is also (alled os FLAT Top SAMPLIN
2()=mt)

Message sign
at)=mt)|
Sgt)
Tran Jnpus
Ts Sg4)
S
gt)
Sampled 8ir)
st)
Pt)
Train pulse
"pt)

PAM Signa
Pulse duahin (t) s()
Fia.1: PULSE AMpLITUDE MoDU LATIoN
L A T I O N t

M,
Dr. Venkatesha Associate Professor, Department of ECE, sVIT venkatesha.m@saividya.ac.in
Principles of Communication Systems SVIT 18EC53 1y

The Wavefrmá § a PA 6ignal is îil usated Fig-1.

L e t S(t) denotes he PAM 8ignal Flat top Sampled 8ignal

I+ is expC 8ed GR

S)= 2 z (nTs). P(L-nTs)

0)
wheaf,
nTs) : e Sample álue t ) obtained at time
nTs
Ts: Sampliag pesiod
PC4)tandard eclangulas pulse train of dusatan t '

Dee chim ot PAM Signal

PAM Signal RECONSTRUCTION MesSage

S t )=
EqUALIzER
FILTER siGml

Fig.2: QecosButian of messageSigna fom pAM sJt.

The Original messaqe SIgnal, met) = 2lt) is dbBained
fflter followe
passing PAM 81gnalrough the econstucionm
byeualizers Zhoun s Figue.2.

Advantages pAMM:
L T i8 a baxe fe all the dgitel modulahan technigues
lo
L TsarBmi Her & Receiver circurtj fs Simple and eay ConRbuH

Dis Advantages of PAM

BANDWIDTH tog transmissitn
L It Requirs high

Varyin9 sotere iz a
Noise
Signal, amplitude keeps
,
T o PM
CBOLiakd i h t
L sNR is Less.
Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT venkatesha.m@saividya.ac.in
Principles of Communication Systems SVIT 18EC53 5

45:T IME DIVISION MULTIPLEXING TDM):

VTUMODEL Qp Man
WTth a neat diaqram explain the Cencept ofTDM.

Time Dvision Multiplex ing is a mehod o tranmHHng dod

Teceiving ndependent 8ignak over a coman channel b

means ot &ynchronied gwitdhes at each end of tsan8missio
ine such that each Signal appears on he fne bnly a frach on
Z
of me t an aHena ive pattern.

Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT

venkatesha.m@saividya.ac.in
Principles of Communication Systems SVIT 18EC53 16

Figure 1, 8how he block diaam ¢ TDM 48l+m

h e Concept ot TDM 6 Tllshtted fn Figux.1

A t Message inpu, the low pass P7Iks ax u ed 6 oemove

high treuenuy coempenenß Present he message ignal
The ouhput of e PRE-ALIAS Files f6
ae hen fed a Cemmute tor,|
hich is TAually mplemented aing elecoonic toitehing Ciocti
VFunGh oo oeoMMUTA TOR
V

T
Too Cole a naaDw AAmple in each of the N-message igra3
at a ra of fs>aW.
T o $equeatia)ly lesleave (MULTIPLEX), N-^amples fob
each o he
message S?gral imidea Samplhna inesval TsP
The MulHplexed &ignal lsthen applied lb a AulBe Amplitude maduki

.The pulke Ampli tude Modulatur ,transferms the nulHplexed Eignal

inb a fon Sui table fa trasmissim dver a Conanun ica Hin channel

At Ie eetving end, te polke anp'tude dernodul ata pes fosms

the Tevesse opesaHn of pAM.

Decoownutatx dizibulez the 6ignals he aPpPopriat

Low pass reconstutionPi1lesg at a Da o fs 2N.

The Decommulats 6pesara nyncha

chapni3aHim i e
Connnuta tusr
The econButron f+Hes gves lFe e3Hmaed message

Sgna.

Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT venkatesha.m@saividya.ac.in

Principles of Communication Systems SVIT 18EC53

46 PULSE PoSITION MoDULATIDN*VTUMoDEL QP

mMmmm {PPM) 5Masks
H i t oneat block diaqrama explan the GeneraHon and
Deechom of PpM- INaves
L

i
essage SAMPLE ut) vt) THRESHOLD
PULSE PPM
&
HoLD ADDER SHAPN 6
Signa DETECTOR FILTER $3
mct) | cicuit St

PULSE SAN
ToOTH
eENERATOR | GENERATDbR
Fi9 1 GeneratHon of PPM Waves.

Generaton of PPM Waves,-

Waves i3 zhown fa F91.
TRe Blocx diaqram fo generating ppM
Ta puke potion Modulation <PPM), tke posiHon a pule
relaHve ts i unmodulated -tme oOccu anta is Varied fm
aecordance k the message ignal 8 shown n Fi9 2 (
Amlt)
a) Modulatiog lmessage
siqna)
AP4)

( Puse Caiea

stt)

Dr. Venkatesha M, Associate

nJUL
Fi3.2 PPM WaVe
Professor, Department of ECE, SVIT
C PPM have

venkatesha.m@saividya.ac.in
Principles of Communication Systems SVIT 18EC53 18
F e Message 8ignal m(4), is Piost Converted fnb a PAM Signa)

by uslng SAMPLE HoLD Circuit

S 8houn
Sample & Hold elotuit, gives a 8taisCoße Wavefor n ut)
lo Figu 3 ( fox the message 8gna) n t ) ghon in Pig 3 (a).

in he
TFe 8tgnad ut), îs added tb a Sawtoth wave, Resul
Combine d 6ignal vct),as ghouon fn Plg 3d)
naaow
|L V) i8 applied lo a tiaeshol d deecus hat pwdxes a Veay
Pule at each Hme v ) C0Sse s ew mthe Negative g»nadrehen

TFe7Fe Pe3uthng- sequere of mpulses , fct) is shoun » ffa 3e).

Final, he PPM ignal st) fa generated b siog Reaente

fmpulses, ic+)
tt) is passed hough puke Bhaptg fi Her. fo pooduke
PPM Waves SqW oih
Ne

An(t)
(a)

>t
Mess age &ign

Auct)

(b) ict) e

Sfair g
61gna Fig:3 Generdtin dPPM wave
(a) Message &ignal S4eiaGBe igna) Cawtuth tave
d) vct) : (b)+ ce)
Ce) ppM 8igna
Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT
venkatesha.m@saividya.ac.in
Principles of Communication Systems SVIT 18EC53

DETECTION OF PPM WaveR-

Consider a PPM ave S(#) Lit5 uaifo%an Samplng.
LIMIED.
ASS ue hat the message gignal met) ig aticy BAND

The Fundion PPM vecelves Tz o follolS;

Con vest the vecBfved pPM wave fnld a puße-duaha

Modulaed (PDM) wave wik the Same modulaion
tTateqrat PD M ave vsia a device toilß a Psni
inHegrtien tFme, there by compuHog the area nder each
Puke f re PDM wave.
np a n ple ke outpur he ttegratr at a TmifvamTa
to poDduce a pM W a e , zohoZR pulze amplikud e d*

propoaHonad 6 e 4ig nal Aamples m(nTs) of h

O7fginal PPM 0ae Stt)
fv Demodula he p4M a 3fcoer he signal ignal

PPMWave

PDM Wae
Tnkgratu
Sample (Ps aw)
PAM Wave (m(Ts)

Pulge-Amplitude"
Delt Ctuo

m+) RetovPred sgna

met) From»

Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT venkatesha.m@saividya.ac.in

Principles of Communication Systems SVIT 20
18EC53

46-1 NOISE IN PULSE pasITIDN MODULA TION-* VTUMODELRP"|

DegcTibe the ePPect of NoIse on a pulge pos? han Modulahon
Hem 5 Mar
Ia a
5pkm, the-rasmi ted tmformaion 18 Cenlaine d
PPM
in the e
lotfve pORitenB P he modwakd pulses.
Tke presence op addve Noize affe cg Ihe peoformanca
uch a &skm

e 9utput ignal s noise Tato, agsuming a full-load

nusoidal modulation is gen by

(SNR) TBA
32 No
TRe
Average noise poder m a messa ge bndwidth enw° iz
ewal wN.
The chaanel Signal Noise Ratio (SNR), ts ;
3A
(SNR) 4T BN -(
IG

- BT BT SBT
Ff Ampli hude Kpecm oqa
Raised GRne pula
The
the Frgux Merft f a ppM Bptn i a ai'sed (osine
Puk as 8honn tn tig
Frgue ot MeoitSNR -AB A4 Ts BTWN
SNR) 3 No 3
(FoM)=(
PPM
)B tw END MoDULE-4
Dr. Venkatesha M, Associate Professor, Department of ECE, SVIT
venkatesha.m@saividya.ac.in