Table Of ContentCODEBOOKBASEDBROADBANDAUDIOCODER
USINGWAVELETTRANSFORMS
BY
KWANGRIPHYUN
ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL
OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT
OFTHEREQUIREMENTSFORTHEDEGREEOF
DOCTOROFPHILOSOPHY
UNIVERSITYOFFLORIDA
1996
Tomyfamily;
mycaringfatherandlovingmother,
mybigbrotherandsisters
ACKNOWLEDGEMENTS
IwouldliketoexpressmygratitudetowardmyadvisorDr.HaniphA.
Latchman.Withouthissupportandencouragement,Iwouldhaveneverbeen
abletocompletethisdissertation. IthankmembersofmyPh.D.committee,
Drs. Donald G. Childers, A. Antonio Arroyo, Andrew Laine, and Oscar
Crisalle,fortheirprecioustimeandcomments.InadditionIshouldexpress
myappreciationtoDr.SubramaniaSudharsananforhispricelessadvice.
IamgratefulforthefinancialsupportfromIBMCorporationasanIBM
GraduateFellowshiprecipientforthelastthreeyearsofthePh.D.programat
theUniversityofFlorida.
DuringtheprogramIwasindebtedtomanyfriendseitheracademically
I
orsocially. Tonameafewofthem.Dr.MinsooHahnandDr.SoonN.Huh
werealwaysnearbyforvaluableadvice.Manypeopleprovidedacomfortof
beingfriends, Dr. Sungjong Choi, Dr. Hyounsoo Kim, Dr. Dongwook Suh,
YoungjinMa,andothers.WithoutanyofthemtheexperienceatGainesville
wouldhavebeenlessenjoyable.
Lastlybutmostly,Iwouldhketoexpressmydeepappreciationtomy
familyfor their endless love; mycaringfather and loving mother, mybig
brotherandsisters.Theyhavebeenessentialpartsofmylifeandarefresh
sourcesofenergyandideas.
iii
TABLEOFCONTENTS
pa^es
ACKNOWLEDGEMENTS
iii
ABSTRACT
vii
CHAPTERS
I INTRODUCTION 1
1.1 FourierRepresentationofSignals 1
1.2 AudioCompression 3
j
' 1.3 Objectives 4
1.4 Overview 5
j
II LITERATURESURVEY 6
j , 2.1 BaseWavelets 6
y 2.2 Psychoacoustics 7
2.3 Optimization 3
2.4 BroadbandAudioCoding 10
III MOTIVATION 15
3.1 FourierTransformanditsTime-FrequencyLocalization 15
I
' 3.1.1 VariationsinFourierTransforms 15
3.1.2 GaborTransform 17
3.1.3 Time-FrequencyLocalizationofSTFT 21
3.1.4 ComparisonswithActualData-AnExample 25
3.2 WaveletTransformanditsTime-FrequencyLocalization 30
3.2.1 WaveletTransform-Definition 30
iv
3.2.2 Time-FrequencyWindowofWaveletTransform 33
3.3 MultiresolutionRepresentation 35
3.3.1 MathematicalProperties 35
3.3.2 ImplementationofMultiresolutionRepresentation.... 35
3.3.3 CompactlySupportedWavelet 42
3.4 PsychoacousticalModeling 44
3.4.1 TransformationofFrequencytoCriticalBandRate ... 45
3.4.2 TransformationofLeveltoSpecificLoudness 49
3.4.3 PostmaskingEffects 53
3.4.4 SpecificLoudnessvs.CriticalBandRatevs.Time 56
3.5 EvolutioninSpeechCoding 57
3.6 SystemProposition 61
IV APPROACHESANDSIMULATIONS 64
4.1 SelectionofBaseWavelet 64
4.1.1 Orthogonality 64
4.1.2 Linearity 66
4.1.3 PropertiesofMeyer'sWaveletandLemarie'sWavelet 66
.
4.1.4 DaubechiesWaveletwithCompactSupport 70
4.1.5 PerformanceComparison:LemarieWaveletvs.
DaubechiesWavelet 79
4.1.6 DaubechiesWaveletswithVanishingMoments 86
4.2 JustificationforanEfficientQuantizationAlgorithm 91
4.2.1 CompressionRatio 91
4.2.2 VectorQuantization 92
4.3 FrequencySegmentation 95
! 4.4 SelectionofCodebook 99
4.5 FrequencySignature 101
4.6 Optimization-Trial1 103
4.7 ProgressiveSubframes 106
4.7.1 LengthofInputAudioFrame 106
4.7.2 GroupingofSubbands 107
4.7.3 EnergySpreadamongNarrowBandSignals 116
V
4.7.4 SelectionofCodebook 118
4.8 Optimization-ProgressiveSubframes 118
4.9 BufferHandling 122
V RESULTSANDCONCLUSION 123
5.1 Procedure 123
5.2 Results 125
5.2.1 InputSignals 125
5.2.2 StationarySignals 128
5.2.3 Non-StationarySignals 141
5.3 Contributions 141
5.3.1 SubbandAnalysis 142
5.3.2 CodebookBasedApproximationofSubbandSignals.. 142
5.3.3 ProgressiveSubframing 143
5.3.4 BandwidthRequirement 144
5.3.5 ScalableAudio 145
j ^
! 5.3.6 ImplementationofMaskingEffects 145
5.4 Conclusions 146
VI FUTUREWORK 147
6.1 SystemDesignBasedonPsychoacoustics 147
6.2 OptimalCodebook 148
6.3 TimeWindow 149
6.4 PsychoacousticalDynamicQuantizer 150
6.5 MaskingEffects 151
1 6.6 ResearchonBaseWavelets 151
APPENDIX
ENERGYDISTRIBUTIONOFNARROWBANDSIGNALS
.
REFERENCES
BIOGRAPHICALSKETCH
vi
i1 :
i
!i : AbstractofDissertationtotheGraduateSchool
! oftheUniversityofFloridainPartialFulfillmentofthe
RequirementsoftheDegreeofDoctorofPhilosophy
I
CODEBOOKBASEDBROADBANDAUDIOCODER
USINGWAVELETTRANSFORMS
KwangRipHyun
j
' May1996
Chairman:HaniphA.Latchman
MajorDepartment:ElectricalandComputerEngineering
I Thisdissertationproposesadifferentapproachtorepresentbroadband
audio signals. Conventional audio coding algorithms such as the MPEG
perform a filter bank analysis and apply a psychoacoustically designed
d1yn'amic quantization on each subband signal. On the other hand, the
proposedalgorithmperformsasubbandanalysisoninputaudiousingwavelet
transforms,andtheresultingsubbandsignalsarerepresentedbytheoptimal
codewordsfromthepredeterminedcodebook.Bycarefullyselectingthebase
wavelet and the analysis tree structure the subband analysis is achieved
accordingtothecriticalbandconcept. Overall, the systemisbased onthe
provenideathatthetimevaryingspecificloudnessalongthecriticalbands
containssufficientinformationtoreproducethetransparentaudiooutput.
vii
Thesampleaudiofilesofvariousmonotonesandtheircombinationsare
processedthroughtheproposedsystem.Theoutputsarevirtuallytransparent
tohumanearspsychoacousticallyeventhoughactualmusicsignalsneedsome
further refinements. The overall performance ofthe codebook based audio
coderexhibitsagreatpotential.Thecurrentsystemisnotoptimizedforahigh
compressionratio,butwithadynamicquantizerinplacethecompressionis
expected to be high. Furthermore, the output coefficients allow an easy
implementationofthepsychoacousticalideasincludingmaskingeffectssince
theyaredirectlyrelatedtothefrequencycomponentsofagiveninputaudio
frame.
Wehaveknowinglyundertakenamammothtasksincemanytensof
man-years wereputintodevelopingandrefiningtoll-qualityspeechcoders,
andthusweknowmuchworkwillneedtobedoneinoptimizingthecodebook
approach for high fidelity audio. Nonetheless, the method presented here
represents a first step in this direction and provides a demonstration of
mathematicalandpracticalfeasibilityofthecodebookapproachaswellasa
platformforfurtherrefinements.
viii
CHAPTER
I
INTRODUCTION
1.1 FourierRepresentationofSignals
j
The representation of signals by sums of complex exponentials of
sinusoidsleadstoconvenientsolutionstoproblemsinmanyareasofscience
andengineering. Itoftenprovides greaterinsightintophysicalphenomena
thanisavailablebyothermeans.SuchFourierrepresentationsarecommonly
usedtodeterminetheresponseoflinearsystemstoasuperpositionofcomplex
exponentialsorsinusoids.Asanexample,speechcommunicationresearchis
one area where the concept ofa Fourier representation has traditionally
playedamajorrole.Theproductionofasteadystatespeechsoundsuchasa
vowelorfricativesimplyconsistsofahnearsystemexcitedbyasourcewhich
iseitherperiodicallyorrandomlyvaryingwithtime.Ifsuchamodelmeets
certain rules in general [Rab78], the spectrum ofthe outputwouldbe the
productofthefrequencyresponseofthevocaltractsystemandthespectrum
ofthe excitation. Based on the same principle, when the input signal is
representedbythesumofcomplexexponentials,thespectrumoftheoutputof
such a model is constructed by the sum of the output to each complex
exponentialinput.
1
2
A major drawback ofthe Fourier representation is that it does not
admit an appropriate representation of the transient characteristics of
signals. This can be seen from the definition ofthe discrete-time Fourier
transformgivenby
oo
X(e>«)= X ^(^)e-^'"". (1.1)
n——oo
Thetimeintervalof(-00,00)isrequiredtocharacterizesuccessfullythesignal
Also,ifthereisalocalvariationsuchasanimpulse,theimpactofsucha
rapidchangespreadsovertheentirefrequencyspectrum.Thelocalizationof
sudden changes within signals is required in order to process them with
transientvariations.
Another disadvantage of Fourier transform is that the frequency
resolutionstaysconstantwhenitiscomputedonadigitalcomputer.Foran
example,supposethatthereisaband-limitedsignalwhosesamplingrateis
20KHz,andthata1024-pointfastFouriertransform(FFT)isperformedon
thesignal.TheoutputoftheFFTshowsthefrequencyspectrumoftheinput
signal in the digital domain. Here, the frequency resolution between each
pointiscalculatedapproximatelyaslOKHz/512samples=19.53Hz/sample.
Afineresolutionisusuallypreferredtomonitorlowfrequencycharacteristics
andarelativecoarseresolutionisallowedtoscanhighfrequencybehaviorsof
inputsignalsincehumansensorsworkinthelogarithmicscale[Zwi90].One
waytoadjustthefrequencyresolutioninthedigitaldomainistochoosea
different number ofpointsonthe FFTorchange the samplingrate ofthe
