8/3/2019 25_Audio Coding 2
1/27
MULTIMEDIASYSTEMSLecture25
SreerajK.P.
Asst.Professor,
DEC,RSET
8/3/2019 25_Audio Coding 2
2/27
Polyphase
filterimplementation
8/3/2019 25_Audio Coding 2
3/27
Introduction
Twoapproachestoanalysissynthesis
filterdesign Directimplementationoffilterbanksintimedomain(throughFIRfilters)with
overlappedfrequencydomain
characteristics. requirefrequencydomainaliascorrectionby
theproperdesignofadjacentfilterbank
characteristics.
WindowtheinputsamplesandtransformsthosethroughDCT/DST.
requiretimedomainaliascorrection.
8/3/2019 25_Audio Coding 2
4/27
TheoryofPolyphasefilters Designofamultibandfilterrequiresalias
cancellationbetweenadjacentbandsand
thatthefiltershapesbecontrolledsuchthatthetransitionbandsofadjacentfilters
addtoproduceaflatresponse.
Thiscanbeformedbyfirstdesigningalowpassprototypefilterwithacontrolled
transitionbandfrequencyresponse.
Thefilterbankcanthenbecomposedby
multiplyingtheimpulseresponseoftheprototypelowpassfilterwithasinusoid
havingfrequenciesequaltothecentre
frequenciesofthedesiredfilters.
8/3/2019 25_Audio Coding 2
5/27
TheoryofPolyphasefilters
AbankofMfilterstobesynthesized
isshown
8/3/2019 25_Audio Coding 2
6/27
TheoryofPolyphasefilters
Realbandpassfiltersarecomposed
oftwocomplexfiltersFi(z)andGi(z)locatedrespectivelyatthepositive
andnegativecentrefrequencies.
IftheprototypelowpassfilterisaFIR
filterwithimpulseresponseh(n)and
z-transformH(z)then
8/3/2019 25_Audio Coding 2
7/27
TheoryofPolyphasefilters
Weobtainabandoffilerswith
i=0,1.M-1andthecorrespondingcompositefiltersare
whereai,bi,cianddiarecomplex
constants
8/3/2019 25_Audio Coding 2
8/27
TheoryofPolyphasefilters
theanalysisandthesynthesisfilter
banksisshownas
Ifai=bi*
8/3/2019 25_Audio Coding 2
9/27
TheoryofPolyphasefilters
hi(n)containsoddnumberofhalf
cyclesofsinusoidsin2Mpoints Iftheinputsamplesaregivenbyx(n),
n=0,1,.,thenfilteredoutput
L:lengthoffiltertap
Substitutingequationhi(n)insi(n)weobtainDCT/DSToftheinputsamples,
multipliedbytheprototypelowpass
filtersimpulse.
8/3/2019 25_Audio Coding 2
10/27
TheoryofPolyphasefilters Theresponseofeachbandiisa
modulationoftheprototyperesponsewith
acosinetermtoshiftthelowpassresponsetotheappropriateband.
Hence,thesearecalledpolyphasefilters.
8/3/2019 25_Audio Coding 2
11/27
TheoryofPolyphasefilters
Theinputsamplesarefirstmultiplied
bylowpassprototypefilterh(n). Blocksof2Mproductsofthe
multiplicationsareaccumulatedwith
thesignofalternateblocksnegated.
These2Mvaluesarethenmultiplied
byMsinusoidstogeneratetheM
outputvalues.
8/3/2019 25_Audio Coding 2
12/27
TheoryofPolyphasefilters
A typical response of low-pass prototype analysis filter h(n)
Windowing function c(n)
8/3/2019 25_Audio Coding 2
13/27
PolyphaseanalysisfilterforMPEG-1audio
Polyphase implementation of analysis filter bank
8/3/2019 25_Audio Coding 2
14/27
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
8/3/2019 25_Audio Coding 2
15/27
PolyphasesynthecsisfilterforMPEG-1
audio
Polyphase implementation of synthesis filter bank
Pol phase s nthecsis filter for MPEG 1
8/3/2019 25_Audio Coding 2
16/27
The32subbandsamplesaretransformed
backtothe64elementVvector,usinginverseMDCT(IMDCT).
TheV-vectorispushedintoaFIFOwhichstoresthelast16Vvectors.
AU-vectoriscreatedfromthealternate32componentblocksandawindow(calledD-window)isappliedtoUtoproducetheW-vector,whichisdividedinto16vectors,
eachhaving32values. These16vectorsareaddedtogethertoobtain32sampleoutput.
PolyphasesynthecsisfilterforMPEG-1audio
8/3/2019 25_Audio Coding 2
17/27
PsychoacousticModels
8/3/2019 25_Audio Coding 2
18/27
Psychoacousticmodelclassification
Model 1: iscomputationallysimple.
hashighaccuracyathighbitrate.
Model 2: iscomputationallycomplex.
hashighaccuracyatlowbitrate.
8/3/2019 25_Audio Coding 2
19/27
Psychoacousticmodelclassification
Essentialphilosophiesofboththe
models:
ComputeFourierpowerspectrumofthe
signal.(512pointFFTforlayer1&2/
1024pointFFTforlayer3).
Mapthespectrumintocriticalbanddomain.
Distinguishbetweenthetonalandnon-
tonalcomponents. Calculatethemaskingfunction.
Mapthesefunctionsbacktothesub-
banddomain.
P h i d l I
8/3/2019 25_Audio Coding 2
20/27
PsychoacousticmodelI Theauditoryspectrumisapproximatedbyalistoftonalandnon-tonalcomponents.
Tonalcomponentsareselectedbyidentifyingthemaximainthespectrumwhoseheightisgreatestintheneighbourhood.
Alltheremainingspectrallinesareusedfor
calculatingthenon-tonalcomponents.Theyaregroupedintocriticalbands.Withineachcriticalband,anon-tonalcomponentisrepresented.
Then,thelistoftonalandnoisecomponentsaredecimatedbyeliminatingthosecomponentswhicharebelowtheauditorythresholdorarelessthanonehalfofacriticalbandwidthfromaneighbouringcomponent.
P h i d l I
8/3/2019 25_Audio Coding 2
21/27
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
8/3/2019 25_Audio Coding 2
22/27
PsychoacousticmodelI
Tonal masking index
Non- tonal masking index
P h ti d l I
8/3/2019 25_Audio Coding 2
23/27
PsychoacousticmodelI
P h ti d l I
8/3/2019 25_Audio Coding 2
24/27
PsychoacousticmodelI
P h ti d l I
8/3/2019 25_Audio Coding 2
25/27
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
8/3/2019 25_Audio Coding 2
26/27
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.
8/3/2019 25_Audio Coding 2
27/27
PsychoacousticmodelII
Itdoesnotmakeadistinctionbetweenthe
tonalandnon-tonalcomponents. Spectraldataistransformedintoa
partitiondomain.
1024pointFFTcomputationisused.
Tonalityisdecidedbytheunpredictability
ofthespectrumwithtime.
Top Related