wavelet_transform_and_properties.pdf

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1、Sheng,Y.“WaveletTransform.”TheTransformsandApplicationsHandbook:SecondEdition.Ed.AlexanderD.PoularikasBocaRaton:CRCPressLLC,200010WaveletTransformYunlongSheng10.1IntroductionLavalUniversityContinuousWaveletTransform•Time-FrequencySpaceAnalysis•Short-TimeF

2、ourierTransform•WignerDistributionandAmbiguityFunctions10.2PropertiesoftheWaveletsAdmissibleCondition•Regularity•MultiresolutionWaveletAnalysis•LinearTransformProperty•ExamplesoftheWavelets10.3DiscreteWaveletTransformTime-ScaleSpaceLattices•WaveletFrame10

3、.4MultiresolutionSignalAnalysisLaplacianPyramid•SubbandCoding•ScaleandResolution10.5OrthonormalWaveletTransformMultiresolutionAnalysisBases•OrthonormalBases•OrthonormalSubspaces•WaveletSeriesDecomposition•Reconstruction•BiorthogonalWaveletBases10.6FilterB

4、ankFIRFilterBank•PerfectReconstruction•OrthonormalFilterBank•OrthonormalFiltersinTimeDomain•BiorthogonalFilterBank10.7WaveletTheoryOrthonormality•Two-ScaleRelationsinFrequencyDomain•OrthonormalFiltersinTimeDomain•WaveletandSubbandFilters•Regularity10.8Som

5、eOrthonormalWaveletBasesB-SplineBases•LemarieandBattleWaveletBasis•DaubechiesBasis10.9FastWaveletTransformWaveletMatrices•NumberofOperations•TimeBandwidthProduct10.10ApplicationsoftheWaveletTransformMultiresolutionSignalAnalysis•SignalDetection•ImageEdgeD

6、etection•ImageCompressionABSTRACTThewavelettransformisanewmathematicaltooldevelopedmainlysincethemiddleofthe1980’s.Itisefficientforlocalanalysisofnonstationaryandfasttransientwide-bandsignals.Thewavelettransformisamappingofatimesignaltothetime-scalejointre

7、presentationthatissimilartotheshort-timeFouriertransform,theWignerdistributionandtheambiguityfunction.Thetemporalaspectofthesignalsispreserved.Thewavelettransformprovidesmultiresolutionanalysiswithdilatedwindows.Thehighfrequencyanalysisisdoneusingnarrowwi

8、ndowsandthelowfrequencyanalysisisdoneusingwidewindows.Thewavelettransformisaconstant-Qanalysis.©2000byCRCPressLLCThebaseofthewavelettransform,thewavelets,aregeneratedfromabasicwaveletfunctionbydilationsandtranslatio