25_Audio Coding 2

8/3/2019 25_Audio Coding 2

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MULTIMEDIASYSTEMSLecture25

SreerajK.P.

Asst.Professor,

DEC,RSET


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Polyphase

filterimplementation


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Introduction

Twoapproachestoanalysissynthesis

filterdesign Directimplementationoffilterbanksintimedomain(throughFIRfilters)with

overlappedfrequencydomain

characteristics. requirefrequencydomainaliascorrectionby

theproperdesignofadjacentfilterbank

characteristics.

WindowtheinputsamplesandtransformsthosethroughDCT/DST.

requiretimedomainaliascorrection.


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TheoryofPolyphasefilters Designofamultibandfilterrequiresalias

cancellationbetweenadjacentbandsand

thatthefiltershapesbecontrolledsuchthatthetransitionbandsofadjacentfilters

addtoproduceaflatresponse.

Thiscanbeformedbyfirstdesigningalowpassprototypefilterwithacontrolled

transitionbandfrequencyresponse.

Thefilterbankcanthenbecomposedby

multiplyingtheimpulseresponseoftheprototypelowpassfilterwithasinusoid

havingfrequenciesequaltothecentre

frequenciesofthedesiredfilters.


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TheoryofPolyphasefilters

AbankofMfilterstobesynthesized

isshown


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Realbandpassfiltersarecomposed

oftwocomplexfiltersFi(z)andGi(z)locatedrespectivelyatthepositive

andnegativecentrefrequencies.

IftheprototypelowpassfilterisaFIR

filterwithimpulseresponseh(n)and

z-transformH(z)then


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Weobtainabandoffilerswith

i=0,1.M-1andthecorrespondingcompositefiltersare

whereai,bi,cianddiarecomplex

constants


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theanalysisandthesynthesisfilter

banksisshownas

Ifai=bi*


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hi(n)containsoddnumberofhalf

cyclesofsinusoidsin2Mpoints Iftheinputsamplesaregivenbyx(n),

n=0,1,.,thenfilteredoutput

L:lengthoffiltertap

Substitutingequationhi(n)insi(n)weobtainDCT/DSToftheinputsamples,

multipliedbytheprototypelowpass

filtersimpulse.


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TheoryofPolyphasefilters Theresponseofeachbandiisa

modulationoftheprototyperesponsewith

acosinetermtoshiftthelowpassresponsetotheappropriateband.

Hence,thesearecalledpolyphasefilters.


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Theinputsamplesarefirstmultiplied

bylowpassprototypefilterh(n). Blocksof2Mproductsofthe

multiplicationsareaccumulatedwith

thesignofalternateblocksnegated.

These2Mvaluesarethenmultiplied

byMsinusoidstogeneratetheM

outputvalues.


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A typical response of low-pass prototype analysis filter h(n)

Windowing function c(n)


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PolyphaseanalysisfilterforMPEG-1audio

Polyphase implementation of analysis filter bank


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PolyphaseanalysisfilterforMPEG-1audio

Theaudiosignalisshiftedintoa512samplesXbuffer,32samplesata

time.

ThecontentofXbufferaremultipliedbytheC-windowfunctionc(n)andthe

resultsarestoredintotheZ-buffer. TheZ-buffercontentsaredividedintoeight64-elementvectors(takingM=32),whicharesummedtoforma64-elementY-vector.

TheY-vectoristransformedusingMDCTtoyieldthe32-subband

samples.

P l h th i filt f MPEG 1


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PolyphasesynthecsisfilterforMPEG-1

audio

Polyphase implementation of synthesis filter bank

Pol phase s nthecsis filter for MPEG 1


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The32subbandsamplesaretransformed

backtothe64elementVvector,usinginverseMDCT(IMDCT).

TheV-vectorispushedintoaFIFOwhichstoresthelast16Vvectors.

AU-vectoriscreatedfromthealternate32componentblocksandawindow(calledD-window)isappliedtoUtoproducetheW-vector,whichisdividedinto16vectors,

eachhaving32values. These16vectorsareaddedtogethertoobtain32sampleoutput.

PolyphasesynthecsisfilterforMPEG-1audio


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PsychoacousticModels


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Psychoacousticmodelclassification

Model 1: iscomputationallysimple.

hashighaccuracyathighbitrate.

Model 2: iscomputationallycomplex.

hashighaccuracyatlowbitrate.


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Psychoacousticmodelclassification

Essentialphilosophiesofboththe

models:

ComputeFourierpowerspectrumofthe

signal.(512pointFFTforlayer1&2/

1024pointFFTforlayer3).

Mapthespectrumintocriticalbanddomain.

Distinguishbetweenthetonalandnon-

tonalcomponents. Calculatethemaskingfunction.

Mapthesefunctionsbacktothesub-

banddomain.

P h i d l I


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PsychoacousticmodelI Theauditoryspectrumisapproximatedbyalistoftonalandnon-tonalcomponents.

Tonalcomponentsareselectedbyidentifyingthemaximainthespectrumwhoseheightisgreatestintheneighbourhood.

Alltheremainingspectrallinesareusedfor

calculatingthenon-tonalcomponents.Theyaregroupedintocriticalbands.Withineachcriticalband,anon-tonalcomponentisrepresented.

Then,thelistoftonalandnoisecomponentsaredecimatedbyeliminatingthosecomponentswhicharebelowtheauditorythresholdorarelessthanonehalfofacriticalbandwidthfromaneighbouringcomponent.

P h i d l I


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PsychoacousticmodelI Tocomputethemaskingeffectofatonalor

non-tonalcomponentontheneighbouring

spectralfrequencies,thestrengthofthecomponentissummedwithtwoterms

calledthemaskingindexandthemasking

function.

Maskingindex:Anattenuationtermwhich

dependsonthecriticalbandrateofthe

componentandwhetheritistonalornon-tonal.

Maskingfunction:Anattenuationfactorwhich

dependson

Displacementofthecomponentfromneighbouring

frequency.

Thecomponentsignalstrength.

P h i d l I


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PsychoacousticmodelI

Tonal masking index

Non- tonal masking index

P h ti d l I


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P h ti d l I


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P h ti d l I


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PsychoacousticmodelI Foratonalcomponentj,atcritical

bandratez(j),themaskingthreshold

LTtm(j,i)atcriticalbandratez(i)is

givenby

LTtm(j,i)=Xtm(j)+avtm(z(j))+vf[z(i)z(j),Xtm(j)] Xtm(j):thestrengthoftonalcomponentat

frequencyj

avtm(j):thetonalmaskingindexatthecritical

bandratez(j),

vf(i,j):themaskingfunction

irepresentingdisplacement

jrepresentingsignalstrength.

P h ti d l I


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PsychoacousticmodelI Fornon-tonalcomponentsthemaskingindexcanbecalculatedas:

LTnm(j,i)=Xnm(j)+avnm(j)+vf[z(i)-z(j),Xnm(j)] Theglobalmaskingthresholdsarecomputedforallspectralfrequenciesbyaddingthemaskingthresholdscomputed

above,foralltheneighbouringtonal&non-tonalcomponents,withthethresholdofhearing.

Theminimummaskingthresholdfunctionis

determinedforeachsub-bandfromtheminimumofalltheglobalmaskingthresholdscontributingtothatsub-band.

Signaltomaskratio(SMR)iscomputed.


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PsychoacousticmodelII

Itdoesnotmakeadistinctionbetweenthe

tonalandnon-tonalcomponents. Spectraldataistransformedintoa

partitiondomain.

1024pointFFTcomputationisused.

Tonalityisdecidedbytheunpredictability

ofthespectrumwithtime.

25_Audio Coding 2

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