3.7.Differen+alPulseCodeModula+on

²  Differen'alPulseCodeModula'on(DPCM)occurscanbeusedwhenadjacentsamplesareclosetothesamevalue.

²  Theremaybealotofredundancyinthesamplesandthereforebandwidthwouldbewasted.

²  Onewaytoavoidthisistoonlytransmitthe“differen'als”.

²  Also,thepresentvaluecanbees'matedfrompastvaluesbyusingapredic'onfilter.

3.7.Differen+alPulseCodeModula+on

Thepresentvaluecanbees'matedfrompastvaluesbyusingapredic'onfilter.

Z(nTs ) = al y(nTs − lTs )l=1

K

∑

3.7.Differen+alPulseCodeModula+on

FirstDPCMconfigura'on:usespredictortoobtainadifferen+alpulseamplitude-modulated(DPAM)signal.

3.7.Differen+alPulseCodeModula+on

SecondDPCMconfigura'on:tominimizethequan'za'onnoiseontherecoveredanalogsignal.

3.7.Differen+alPulseCodeModula+on

SameasPCM,theDPCMfollowsthe6-dBrule

6.02dB

S nN

α⎛ ⎞ = +⎜ ⎟⎝ ⎠

wherenisthebitnumber

ForPCM:α=4.77forpeakSNR,α=0foraverageSNR.

ForDPCM:αhasawiderangedependingontheproper'esoftheinputanalogsignal.Forexample:α=-10dBforμ=255compandedPCM(μ-law)signal.TheSNRimprovementof25dBforDPCM.

3.8.DeltaModula+on

DeltaModula+on(DM)isaspecialcaseofDPCMinwhichtherearetwoquan'zinglevels.It’smainfeaturesare:

²  Thetransmi\eddataarereducedto1-bitdatastream.

²  Theanalogsignalisapproximatedwithaseriesofsegments.

²  Eachsegmentofapproximatedsignalisdeterminedbycomparison.

² Onlythechangeofinforma'onissent.Generallyspeaking,“1”indicateamplitude“increasing”,and“0”indicateamplitude“decrease”,andalterna've“1”and“0”indicatesamplituderemains.

²  ToachievehighSNR,deltamodula'onmustuseoversamplingtechniques,thatis,theanalogsignalissampledatarateseveral+meshigherthantheNyquistrate.

3.8.DeltaModula+on

3.8.DeltaModula+on

zn =1Vc

δy(iTs )i=0

n

∑

3.8.DeltaModula+on

3.8.DeltaModula+on

3.8.DeltaModula+onGranularNoiseandSlopeOverloadNoise

Thequan'zingnoiseerrorsignalmaybeclassifiedintotwotypesofnoise:slopeoverloadnoiseandgranularnoise

²  slopeoverloadnoise:whenthestepsizeδistoosmall

²  granularnoise:occursforanystepsizeδ.Thesmallerstepthesmallernoise

3.8.DeltaModula+on

Example3-16DesignofaDMsystemFindthestepsizeδrequiredtopreventslopeoverloadnoiseforthecasewhentheinputsignalisasinewave.

3.8.DeltaModula+on

PSDandNSRofNoise

Granularnoisepowerintheanalogsignalband:

N =< n2 >= pn( f )df =δ2B3 fs−B

B∫

ThePSDforthenoiseis:

pn( f ) =δ2

6 fs

3.8.DeltaModula+onAdeltamodula'on(DM)systemistestedwitha10-kHzsinusoidalsignal,1Vpeak-to-peak,attheinput.Thesignalissampledat10'mestheNyquistrate.a)  Whatisthestepsizerequiredtopreventslopeoverloadandtominimize

granularnoise?b)  WhatisthePSDforthegranularnoise?

3.9.Time-DivisionMul+plexingDEFINIATION:Time-divisionmul'plexing(TDM)isthe'meinterleavingofsamplesformseveralsourcessothattheinforma'onfromthesesourcescanbetransmi\edseriallyoverasinglecommunica'onchannel.

AttheTransmiNer

Ø Simultaneoustransmissionofseveralsignalsona'me-sharingbasis.

Ø Eachsignaloccupiesitsowndis'nct'meslot,usingallfrequencies,forthedura'onofthetransmission.

Ø Slotsmaybepermanentlyassignedondemand.

3.9.Time-DivisionMul+plexing

AttheReceiver

Ø Decommutator(sampler)hastobesynchronizedwiththeincomingwaveformàFrameSynchroniza'on

Ø Lowpassfilter

Ø ISI–poorchannelfiltering

Ø Feedthroughofonechannel'ssignalintoanotherchannel--Crosstalk

Applica+onsofTDM:DigitalTelephony,DataCommunica'ons,SatelliteAccess,CellularRadio.

PulsewidthofTDMPAM: s

s

fT

31

3=

nTs3

PulsewidthofTDMPCM:

s1 satisfies Nyquist ratess

f fT

=

3.9.Time-DivisionMul+plexing