Discrete Cosine Transform, Second Edition PDF
Preview Discrete Cosine Transform, Second Edition
Discrete Cosine Transform Second Edition Discrete Cosine Transform Second Edition Humberto Ochoa-Dom´ınguez K. R. Rao CRCPress Taylor&FrancisGroup 6000BrokenSoundParkwayNW,Suite300 BocaRaton,FL33487-2742 (cid:2)c 2019byTaylor&FrancisGroup,LLC CRCPressisanimprintofTaylor&FrancisGroup,anInformabusiness NoclaimtooriginalU.S.Governmentworks Printedonacid-freepaper InternationalStandardBookNumber-13:978-1-138-30472-7(Hardback) Thisbookcontainsinformationobtainedfromauthenticandhighlyregardedsources.Reasonableefforts havebeenmadetopublishreliabledataandinformation,buttheauthorandpublishercannotassume responsibilityforthevalidityofallmaterialsortheconsequencesoftheiruse.Theauthorsandpublishers haveattemptedtotracethecopyrightholdersofallmaterialreproducedinthispublicationandapologize tocopyrightholdersifpermissiontopublishinthisformhasnotbeenobtained.Ifanycopyrightmaterial hasnotbeenacknowledgedpleasewriteandletusknowsowemayrectifyinanyfuturereprint. ExceptaspermittedunderU.S.CopyrightLaw,nopartofthisbookmaybereprinted,reproduced,trans- mitted,orutilizedinanyformbyanyelectronic,mechanical,orothermeans,nowknownorhereafter invented,includingphotocopying,microfilming,andrecording,orinanyinformationstorageorretrieval system,withoutwrittenpermissionfromthepublishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com(http://www.copyright.com/)orcontacttheCopyrightClearanceCenter,Inc.(CCC), 222RosewoodDrive,Danvers,MA01923,978-750-8400.CCCisanot-for-profitorganizationthatpro- videslicensesandregistrationforavarietyofusers.Fororganizationsthathavebeengrantedaphotocopy licensebytheCCC,aseparatesystemofpaymenthasbeenarranged. TrademarkNotice:Productorcorporatenamesmaybetrademarksorregisteredtrademarks,andare usedonlyforidentificationandexplanationwithoutintenttoinfringe. LibraryofCongressCataloging-in-PublicationData Names:Rao,K.Ramamohan(KamisettyRamamohan),author.|Ochoa-Dom´ınguez, Humberto,author. Title:Discretecosinetransform/HumbertoOchoa-Dom´ınguezandK.R.Rao. Description:Secondedition.|BocaRaton,FL:Taylor&FrancisGroup,CRCPress, 2019.|Revisededitionof:Discretecosinetransform:algorithms,advntages, applications/K.R.Rao,P.Yip.1990.|Includesbibliographicalreferencesandindex. Identifiers:LCCN2019000195|ISBN9781138304727(hardback:alk.paper) Subjects:LCSH:Signalprocessing--Mathematics.|Discretecosinetransforms. Classification:LCCTK5102.5.R3352019|DDC621.382/23--dc23 LCrecordavailableathttps://lccn.loc.gov/2019000195 VisittheTaylor&FrancisWebsiteat http://www.taylorandfrancis.com andtheCRCPressWebsiteat http://www.crcpress.com Acknowledgments Thisbookistheresultofthelongtermassociationoftheauthors, HumbertoOchoa-Dom´ınguez andK.R.Rao.Dr.Ochoa’ssignificant andsustainedcontributionsmadethisbookpossible.Specialthanks gototheirrespectivefamiliesfortheirsupport,perseveranceand understanding.Dr.Ochoawouldliketoexpresshisgratitudeto ClaudiaValenzuela,forhercontinuoussupportduringthewritingof thisbook,andtotheUniversidadAuto´nomadeCiudadJua´rez (UACJ).Dr.Raowouldliketoacknowledgethesupportprovidedin variousformsbyDr.Crouch,DeanoftheCollegeofEngineering,and Dr.J.W.Bredow,Chair,DepartmentofElectricalEngineering,both atUTA.Dr.G.J.Sullivan, Microsoft,Dr.H.Kalva,FloridaAtlantic UniversityandDr.W.-K.Cham,ChineseUniversityofHongKong providedvariousresourcesinthisregard.ShibaKuanar,Harsha Nagathihalli Jagadish,VenkataSivaReddyAnushaandSwaroop KrishnaRaoatUTAcontributed countlesshoursintyingupallloose ends(references,copyrightreleases,proofreadingandamillionother details).ThegraduatestudentsandalumnaeintheMultimedia ProcessingLab(MPL)atUTAinvariouswayshavemade constructivecomments. Contents Preface.....................................................................................................................xiii Acronyms...............................................................................................................xvii Contributors..........................................................................................................xxiii ListofFigures........................................................................................................xxv ListofTables.........................................................................................................xxix Chapter1 Introduction.....................................................................................1 Applications.....................................................................................1 Chapter2 TheKarhunen–Loe`veTransform....................................................5 Introduction......................................................................................5 TheKarhunen–Loe`veTransformfora1DRandomField...............5 EigenvaluesandEigenvectorsofR.........................................7 ApplicationofKLTtoDataCompression.......................................8 KLTfora2DRandomField..........................................................11 Applications...................................................................................17 Summary........................................................................................18 Problems........................................................................................19 Projects...........................................................................................20 Chapter3 TheDiscreteCosineTransform.....................................................23 Introduction....................................................................................23 TheFourierCosineTransform.......................................................24 PropertiesoftheFCT............................................................24 Definitions......................................................................................27 TheUnitarityofDCTs...................................................................29 ScalinginTime..............................................................................33 ShiftinTime..................................................................................34 TheDifferenceProperty.................................................................38 TheConvolutionProperty..............................................................39 RelationtotheKLT........................................................................42 DCT-I....................................................................................43 FastAlgorithms..............................................................................46 DCTviaFFT.........................................................................47 DirectComputationbySparseMatrixFactorizations..........53 vii viii Contents Decimation-in-Time(DIT)andDecimation-in-Frequency (DIF)Algorithms.....................................................57 TheDITAlgorithm..................................................57 TheDIFAlgorithm..................................................63 TheDCTviatheWalsh–HadamardTransform(WHT).......69 TheDCTviatheDiscreteHartleyTransform(DHT)..........71 OtherFastAlgorithms..........................................................73 PrimeFactorAlgorithm(PFA)................................74 AFastRecursiveAlgorithm.....................................79 DCT-IIRealizationviaPlanarRotations.................83 Applications...................................................................................88 Summary........................................................................................88 Problems........................................................................................89 Projects...........................................................................................91 Chapter4 TheDiscreteSineTransform.........................................................95 Introduction....................................................................................95 TheFourierSineTransform...........................................................95 PropertiesoftheFST............................................................96 TheDiscreteSineTransform.........................................................99 TheDiscreteFourierTransformofaSkewedSequence....100 TheDiscreteSineTransformviatheDFT..........................101 FastAlgorithms............................................................................102 TheFastDST-IviatheSSTAlgorithm..............................105 SparseMatrixFactorizationoftheDST-I...........................107 TheSplit-RadixAlgorithmforDST-I................................108 Applications.................................................................................110 Summary......................................................................................110 Problems......................................................................................110 Projects.........................................................................................111 Chapter5 TheModifiedDiscreteCosineTransform...................................113 Introduction..................................................................................113 Definitions....................................................................................113 MDCTastheShiftedDiscreteFourierTransform......................117 PropertiesoftheMDCT...............................................................118 EvenlyStackedMDCT................................................................120 MDCTBlockTransform....................................................121 SymmetryPropertiesofMDCTBlockTransform.............122 MatrixRepresentationoftheMDCT..................................123 OddlyStackedMDCT.................................................................125 MDCTBlockTransform....................................................125 SymmetryPropertiesofMDCTBlockTransform.............126 MatrixRepresentationoftheMDCT..................................128 Contents ix Applications.................................................................................129 Summary......................................................................................130 Problems......................................................................................131 Projects.........................................................................................132 Chapter6 TheIntegerDiscreteCosineTransform......................................133 Introduction..................................................................................133 IntegerDCTMatrix.....................................................................134 TheICTbyDirectScaling..................................................135 H.2644x4and8x8ICTMatrices..........................135 WMV94x4and8x8ICTMatrices........................137 AVS1China8x8ICTMatrix.................................138 H.2654x4,8x8,16x16and32x32ICTMatrices.....139 AVS2 China 4x4, 8x8, 16x16 and 32x32 ICT Matrices.................................................141 VersatileVideoCoding(VVC)..............................143 TheICTbyKernelComponentReplacement....................145 FastAlgorithm.......................................................148 TheLiftingMatrixandtheLiftingStep.............................149 TheIntegerDCT-IIbyLiftingMatrix...................155 Low-ComplexityICT(LCICT)..........................................156 SquareWaveTransform......................................................159 Round-offApproximationofIntDCT.................................162 TheTchebichefPolynomials.......................................................163 Orthogonality......................................................................164 DiscreteTchebichefPolynomials.......................................164 Orthogonality.........................................................165 EvenSymmetry......................................................165 TheDiscreteTchebichefTransform...................................166 4x4and8x8DiscreteTchebichefTransforms....................167 IntegerDiscreteTchebichefTransform..............................168 MetricstoEvaluateaTransform..................................................172 Mean-SquareError.............................................................172 CodingGain........................................................................172 TransformEfficiency..........................................................172 VarianceDistribution..........................................................173 EnergyPackingEfficiency(EPE).......................................173 ResidualCorrelation...........................................................173 Implementations...........................................................................174 Applications.................................................................................185 Summary......................................................................................186 Problems......................................................................................187 Projects.........................................................................................188
The list of books you might like
