This document summarizes different waveform coding techniques used for analog to digital conversion in communications systems. It describes the basic principles and processes of Pulse Code Modulation (PCM), Differential Pulse Code Modulation (DPCM), Delta Modulation (DM), and Adaptive Delta Modulation (ADM). Key steps like sampling, quantization, encoding, and decoding are discussed for each technique. The techniques are then compared in terms of their advantages, disadvantages, and applications in signal transmission.

1. TERM PAPER ON
WAVEFORM CODING
Department of Electronics and Communication Engineering
Assessable Activity Based Learning (AAL)
By:
ALAPAN RANJAN BANERJEE
ROLL NO :- 03
YEAR :- 3RD
YEAR
REGISTRATION NO. :- 161220110132 OF 2016-2017
ST. THOMAS’ COLLEGE OF ENGINEERING AND TECHNOLOGY
Affiliated to
MAULANA ABUL KALAM AZAD UNIVERSITY OF TECHNOLOGY ,WEST BENGAL

2. INTRODUCTION
Althoughhumansare well equippedforanalogcommunications,analogtransmissionisnotparticularly
efficient.Whenanalogsignalsbecome weakbecause of transmissionloss,itishardto separate the
complex analogstructure fromthe structure of randomtransmissionnoise.If youamplifyanalogsignals,
it alsoamplifiesnoise,andeventuallyanalogconnectionsbecometoonoisytouse.Digital signals,
havingonly"one−bit"and"zero−bit"states,are more easilyseparatedfromnoise.Theycanbe
amplifiedwithoutcorruption.Digital codingismore immune tonoise corruptiononlong−distance
connections.Also,the world'scommunicationsystemshave convertedtoadigital transmissionformat
calledpulse code modulation(PCM).PCMisa type of codingthat is called"waveform"codingbecause it
createsa codedform of the original voice waveform.Thisdocumentdescribesata highlevel the
conversionprocessof analogvoice signalstodigital signals.
ANALOG TO DIGITAL CONVERSION
 Sampling:take samplesattime nT
– T: samplingperiod;
– fs= 1/T: samplingfrequency
 Quantization:mapamplitudevaluesintoasetof discrete valueskQ
– Q: quantizationinterval orstep size
 BinaryEncoding
– Converteachquantizedvalue intoabinarycodeword

3. QUANTIZATION
A Q-levelquantizercomparesthe discrete-timeinputx(nT)withitsfixeddigital levels.Itassignsanyone
of the digital level tox(nT) withitsfixeddigital levels.Itthenassignsanyone of the digital level tox(nT)
whichresultsinminimumdistortionorerror.Thisiscalledquantizationerror.Thusthe otputof a
quantizerisa digital level.
 Uniformquantization :-
o the quantizationlevelsare uniformlyspaced
o Applicable whenthe signal isinafinite range (fmin,fmax)
o The entire datarange is dividedintoLequal intervalsof length Q(knownas
quantizationinterval orquantizationstep-size) Q=(fmax-fmin)/L
o Interval i is mappedtothe middle value of thisinterval
o We store/sendonlythe index of quantizedvalue
o There are twotypesof uniformquantization.Theyare Mid-Rise type andMid-Tread
type.
 Non-uniformquantization:-
If the quantizercharacteristicsisnonlinearandstepsize isnotconstantinsteadif it is
variable,dependedonthe amplitudeof inputsignal thenthe quantizationisknownas
nonuniformquantization.
The non-uniformquantizationispracticallyachievedbythe processcalled
COMPANDING.
 COMPANDING:-
o The processof compressionof the signal atthe transmitterandexpansionatthe receiveris
calledascompanding(compressionandexpansion).

4. o In companding,the higheramplitudeanalogsignalsare compressedprecedingtransmission
and thenexpandedinthe receiver.
o Compandingisperformedwiththe helpof three functional blocks,whichare Compressor,
UniformquantizerandExpanderandthe diagramin shownbelow
o The compressorwill compressthe dynamicrange of the signal sothat highdynamicrange
signal can be passedthroughcomponentsof low dynamicrange capability,the uniform
quantizerwill undergothe quantizationprocessof the compressedsignal andthe lastlythe
expanderwillundergo expansionandinvertthe compressionfunctiontoreconstructthe
original signal.
o The expanderhascomplementarycharacteristicsasthatof compressorso that the
compressorinputisequal toexpanderoutputinordertoreproduce the signal atthe
receiver.
o belowillustratesthe input-outputcharacteristicsandcurvesof the compandingprocess,
and itcan be seenthatcompandinghaslinearcharacteristics.
Ideally,we needalinearcompressioncharacteristicsforsmall amplitudesof the inputsignal anda
logarithmiccharacteristicselsewhere.Inpractice,thisisdone byusingfollowingtwomethods:
1. A−law Companding
2. u−law Companding

5.  A−lawCompander
Limitingthe linearsamplevaluestotwelve magnitude bits,the A−law compressionis
definedbythisequation,whereA isthe compressionparameter(A=87.7in Europe),and
x isthe normalizedintegertobe compressed.
 u−lawCompander
Limitingthe linearsamplevaluestothirteenmagnitude bits,the u−law (u−law andMu−
laware usedinterchangeablyinthisdocument)compressionisdefinedbythisequation,
where mis the compressionparameter(m=255 in the U.S. and Japan) andx isthe
normalizedintegertobe compressed.
A−lawstandardis primarilyusedbyEurope andthe restof the world.u−law isusedby NorthAmerica
and Japan
PULSE CODE MODULATION (PCM)
In Pulse Code Modulation,the message signal isrepresentedbyasequence of codedpulses.This
message signal isachievedbyrepresentingthe signal indiscrete form inbothtime andamplitude.

6.  Basic Elementsof PCMcommunication :-
o PCMtransmitter :-
 Low PassFilter
Thisfiltereliminatesthe highfrequencycomponentspresentinthe inputanalog
signal whichisgreaterthanthe highestfrequencyof the message signal,to
avoidaliasingof the message signal.
 Sampler
Thisis the technique whichhelpstocollectthe sample dataatinstantaneous
valuesof message signal,soasto reconstructthe original signal.The sampling
rate mustbe greaterthan twice the highestfrequencycomponent of the
message signal,inaccordance withthe samplingtheorem.
 Quantizer
Quantizingisaprocessof reducingthe excessive bitsandconfiningthe data.
The sampledoutputwhengiventoQuantizer,reducesthe redundantbitsand
compressesthe value.
 Encoder
The digitization of analog signal is done by the encoder. It designates each quantized
level by a binary code. The sampling done here is the sample-and-hold process.
These three sections (LPF, Sampler, and Quantized) will act as an analog to digital
converter.Encodingminimizesthe bandwidthused.
o PCMtransmissionpath:-
 RegenerativeRepeater
Thissectionincreasesthe signal strength.The outputof the channel alsohas
one regenerativerepeatercircuit,tocompensate the signal lossandreconstruct

7. the signal,andalsoto increase itsstrength. Here isthe blockdiagramof
regenerativefilter.
o PCMreceiver:-
 Decoder
The decodercircuitdecodesthe pulse codedwaveformtoreproduce the
original signal.Thiscircuitactsas the demodulator.
 ReconstructionFilter
Afterthe digital-to-analogconversionisdone bythe regenerative circuitandthe
decoder,alow-passfilterisemployed,calledasthe reconstructionfiltertoget
back the original signal.
 Application:-
o The PCM isusedinthe satellitetransmissionsystem.
o It isusedin space communication.
o It isusedin telephony.
o The compact disc (CD) isa recentapplicationof PCM.
 Advantagesof PCMcommunication:-
o PCMprovideshighnoise immunity.
o It ispossible toregenerate the codedsignalalongthe transmissionpath.
o It ispossible tostore the signal.
 Disadvantagesof PCMcommunication:-
o The encoding,decodingandquantizingcircuitryof PCMis complex.
o PCMrequiresalarge bandwidthascomparedto othersystems.

8. DIFFERENTIAL PULSE CODE MODULATION (DPCM)
For the samplesthatare highlycorrelated,whenencodedbyPCMtechnique,leave redundant
informationbehind. PCMrequiresalarge bandwidthascomparedtoothersystems. Toprocessthis
redundantinformationand tosave bandwidthDPCMis introduced.
 Basic Elementsof DPCMcommunication:-
o DPCMtransmitter :-
The predictorproducesthe assumedsamplesfromthe previousoutputsof the
transmittercircuit.The inputtothispredictoristhe quantizedversionsof the input
signal.Predictorinputisthe sumof quantizeroutputandpredictoroutput.
o DPCM receiver:-
The predictorassumesa value,basedonthe previousoutputs.The inputgiventothe
decoderisprocessedandthatoutputis summedupwiththe outputof the predictor,to
obtaina betteroutput.

9.  Advantagesof DPCMcommunication:-
o As the differencebetweenx(nT) andx*(nT) isbeingencodedandtransmittedbythe PCM
technique asmall differance voltageistobe quantizedandencoded,thiswill needless
numberof quantizationlevelsandhence lessnumberof bitstorepresentthem
o Thus signalingrate andbandwidthof aDPCMwill be lessthanthat of PCM
 Disadvantagesof DPCMcommunication:-
o Highbit rate
o Practical usage is limited
o Need the predicator circuitto be used which is very complex
DELTA MODULATION
The type of modulation,where the samplingrate ismuchhigherandin whichthe step size after
quantizationisof a smallervalue Δ,sucha modulationistermedasdeltamodulation.
If Mk > Mk-1  take 1
If Mk < Mk-1  take 0
 Basic Elementsof deltamodulation :-
o Transmitter :-
The predictorcircuitin DPCMisreplacedbya simple delaycircuitinDM.
From the above diagram, we have the notationsas−
x(nTs)=oversampledinput
ep(nTs)=summeroutputandquantizerinput
eq(nTs) =quantizeroutput= v(nTs)v(nTs)
xˆ(nTs) = outputof delaycircuit
u(nTs) = inputof delaycircuit

10. o Receiver:-
From the above diagram,we have the notationsas –
vˆ(nTs) isthe inputsample
uˆ(nTs) isthe summeroutput
x¯(nTs) isthe delayedoutput
A binary sequence will be givenasan inputtothe demodulator.The stair-case
approximatedoutputisgiventothe LPF.
 Advantage :-
o Since.Deltamodulationtransmit1bit forone sample,thereforethe signalingrate and
transmissionbandwidthisquite small.
o Very easydesignof the modulatorandthe demodulator
 Disadvantage :-
o If signal changesveryfast“overloadslope noise”occurs.
o If signal changesveryslow“granularnoise”occurs.
ADDAPTIVE DELTA MODULATION
In orderto overcome the quantizationerrors due toslope overloadandgranularnoise,the stepsize (Δ)
ismade adaptive tovariationsinthe inputsignal x(t).Particularlyinthe steepsegmentof the signal x(t),
the stepsize isincreased.Andthe stepisdecreasedwhenthe inputisvaryingslowly.Thismethodis
knownas Adaptive DeltaModulation(ADM).The adaptive deltamodulatorscantake continuous
changesinstepsize or discrete changesinstepsize.

11.  Basic Elementsof deltamodulation:-
o Transmitter :-
The logicfor step size control isaddedinthe diagram.The stepsize increasesor
decreasesaccordingtoa specifiedrule dependingonone bitquantizeroutput.
o Receiver:-
The receiverhastwoportions.The firstportionproducesthe stepsize fromeach
incomingbit.Exactlythe same processisfollowedasthatintransmitter.The previous
inputandpresentinputdecide the stepsize.Itisthenappliedtothe secondportioni.e.,
an accumulatorwhichbuildsupstaircase waveform.The low passfilterthensmoothens
out the staircase waveformtoreconstructthe original signal.
 Advantages:-
o The signal to noise ratioof ADMis betterthanthat of DM because of the reductionin
slope overloaddistortionandidle noise.
o Because of the variable stepsize ,the dynamicrange of ADM is widerthanDM.
o Utilizationof bandwidthisbetterinADMthan DM.

12.  Disadvantages :-
o Implementationof stepsize control logiccircuitisnoteasy.
COMPARISONBETWEEN PCM, DELTA MODULATION, ADAPTIVE DELTA MODULATION AND
DEFFERENTIAL PULSE CODE MODULATION
DIFFERENCES BETWEEN WAVEFORMCODING AND SOUCECODING :-
 The waveformcodersare generallydesignedtobe signal independent.
 The waveformcodersare differentfromthe sauce coders.The source codersdependon
parameterizationof the analogsignal inaccordance withan appropriate model forgenerationof
signal.
REFERENCES :-
 https://electronicspost.com
 https://www.quora.com
 https://www.tutorialpoint.com
 https://www.wikipedia.com