Table Of Content

✐ ✐ \ffirs" | 2004/1/28 | 10:00 | page i | #1 ✐ ✐ Chemometrics ✐ ✐ ✐ ✐ ✐ ✐ \ffirs" | 2004/1/28 | 10:00 | page ii | #2 ✐ ✐ CHEMICAL ANALYSIS ASERIESOFMONOGRAPHSONANALYTICALCHEMISTRY ANDITSAPPLICATIONS Edited by J.D.WINEFORDNER VOLUME164 ✐ ✐ ✐ ✐ ✐ ✐ \ffirs" | 2004/1/28 | 10:00 | page iii | #3 ✐ ✐ Chemometrics From Basics to Wavelet Transform FOO-TIMCHAU HongKongPolytechnicUniversity YI-ZENGLIANG CentralSouthUniversity JUNBINGAO UniversityofNewEngland XUE-GUANGSHAO UniversityofScienceandTechnologyofChina ✐ ✐ ✐ ✐ ✐ ✐ \ffirs" | 2004/1/28 | 10:00 | page iv | #4 ✐ ✐ Copyright?2004byJohnWiley&Sons,Inc.Allrightsreserved. PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey. PublishedsimultaneouslyinCanada. 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LibraryofCongressCataloging-in-PublicationData: Chemometrics:frombasicstowavelettransform/Foo-timChau... [etal.]. p. cm.---(Chemicalanalysis;1075) Includesbibliographicalreferences. ISBN0-471-20242-8(acid-freepaper) 1.Instrumentalanalysis---Dataprocessing.2.Instrumentalanalysis---Automation. 3.Wavelets(Mathematics)I.Chau,Foo-tim.II.Chemicalanalysis;v.1075. QD79.I5C442004 543(cid:1).07(cid:1)0285---dc21 2003002429 PrintedintheUnitedStatesofAmerica. 10 9 8 7 6 5 4 3 2 1 ✐ ✐ ✐ ✐ ✐ ✐ \ftoc" | 2004/1/28 | 10:10 | page v | #1 ✐ ✐ CONTENTS PREFACE xiii CHAPTER1 INTRODUCTION 1 1.1. ModernAnalyticalChemistry 1 1.1.1. DevelopmentsinModernChemistry 1 1.1.2. ModernAnalyticalChemistry 2 1.1.3. MultidimensionalDataset 3 1.2. Chemometrics 5 1.2.1. IntroductiontoChemometrics 5 1.2.2. InstrumentalResponseandData Processing 8 1.2.3. White,Black,andGraySystems 9 1.3. Chemometrics-BasedSignalProcessing Techniques 10 1.3.1. CommonMethodsforProcessing ChemicalData 10 1.3.2. WaveletsinChemistry 11 1.4. ResourcesAvailableonChemometricsand WaveletTransform 12 1.4.1. Books 12 1.4.2. OnlineResources 14 1.4.3. MathematicsSoftware 15 CHAPTER2 ONE-DIMENSIONALSIGNALPROCESSING TECHNIQUESINCHEMISTRY 23 2.1. DigitalSmoothingandFilteringMethods 23 2.1.1. Moving-WindowAverageSmoothing Method 24 2.1.2. Savitsky--GolayFilter 25 v ✐ ✐ ✐ ✐ ✐ ✐ \ftoc" | 2004/1/28 | 10:10 | page vi | #2 ✐ ✐ vi contents 2.1.3. KalmanFiltering 32 2.1.4. SplineSmoothing 36 2.2. TransformationMethodsofAnalytical Signals 39 2.2.1. PhysicalMeaningoftheConvolution Algorithm 39 2.2.2. MultichannelAdvantageinSpectroscopy andHadamardTransformation 41 2.2.3. FourierTransformation 44 2.2.3.1. DiscreteFourierTransformation andSpectralMultiplex Advantage 45 2.2.3.2. FastFourierTransformation 48 2.2.3.3. FourierTransformationas AppliedtoSmooth AnalyticalSignals 50 2.2.3.4. FourierTransformationas AppliedtoConvolution andDeconvolution 52 2.3. NumericalDifferentiation 54 2.3.1. SimpleDifferenceMethod 54 2.3.2. Moving-WindowPolynomial Least-SquaresFittingMethod 55 2.4. DataCompression 57 2.4.1. DataCompressionBasedonB-Spline CurveFitting 57 2.4.2. DataCompressionBasedonFourier Transformation 64 2.4.3. DataCompressionBasedon Principal-ComponentAnalysis 64 CHAPTER3 TWO-DIMENSIONALSIGNALPROCESSING TECHNIQUESINCHEMISTRY 69 3.1. GeneralFeaturesofTwo-DimensionalData 69 3.2. SomeBasicConceptsforTwo-Dimensional DatafromHyphenatedInstrumentation 70 3.2.1. ChemicalRankandPrincipal- ComponentAnalysis(PCA) 71 ✐ ✐ ✐ ✐ ✐ ✐ \ftoc" | 2004/1/28 | 10:10 | page vii | #3 ✐ ✐ contents vii 3.2.2. Zero-ComponentRegionsand EstimationofNoiseLeveland Background 75 3.3. Double-CenteringTechniqueforBackground Correction 77 3.4. CongruenceAnalysisandLeast-Squares Fitting 78 3.5. DifferentiationMethodsforTwo-Dimensional Data 80 3.6 ResolutionMethodsforTwo-Dimensional Data 81 3.6.1. LocalPrincipal-Component AnalysisandRankmap 83 3.6.2. Self-ModelingCurveResolutionand EvolvingResolutionMethods 85 3.6.2.1. EvolvingFactorAnalysis (EFA) 88 3.6.2.2. WindowFactorAnalysis (WFA) 90 3.6.2.3. HeuristicEvolvingLatent Projections(HELP) 94 CHAPTER4 FUNDAMENTALSOFWAVELETTRANSFORM 99 4.1. IntroductiontoWavelet TransformandWaveletPacketTransform 100 4.1.1. ASimpleExample:HaarWavelet 103 4.1.2. MultiresolutionSignalDecomposition 108 4.1.3. BasicPropertiesofWaveletFunction 112 4.2. WaveletFunctionExamples 113 4.2.1. MeyerWavelet 113 4.2.2. B-Spline(Battle--Lemarie´)Wavelets 114 4.2.3. DaubechiesWavelets 116 4.2.4. CoifletFunctions 117 4.3. FastWaveletAlgorithmandPacket Algorithm 118 4.3.1. FastWaveletTransform 119 4.3.2. InverseFastWaveletTransform 122 ✐ ✐ ✐ ✐ ✐ ✐ \ftoc" | 2004/1/28 | 10:10 | page viii | #4 ✐ ✐ viii contents 4.3.3. FiniteDiscreteSignalHandlingwith WaveletTransform 125 4.3.4. PacketWaveletTransform 132 4.4. BiorthogonalWaveletTransform 134 4.4.1. MultiresolutionSignalDecomposition ofBiorthogonalWavelet 134 4.4.2. BiorthogonalSplineWavelets 136 4.4.3. AComputingExample 137 4.5. Two-DimensionalWaveletTransform 140 4.5.1. MultidimensionalWaveletAnalysis 140 4.5.2. ImplementationofTwo-Dimensional WaveletTransform 141 CHAPTER5 APPLICATIONOFWAVELETTRANSFORM INCHEMISTRY 147 5.1. DataCompression 148 5.1.1. PrincipleandAlgorithm 149 5.1.2. DataCompressionUsingWavelet PacketTransform 155 5.1.3. Best-BasisSelectionandCriteriafor CoefficientSelection 158 5.2. DataDenoisingandSmoothing 166 5.2.1. Denoising 167 5.2.2. Smoothing 173 5.2.3. DenoisingandSmoothingUsing WaveletPacketTransform 179 5.2.4. ComparisonbetweenWavelet TransformandConventionalMethods 182 5.3. Baseline/BackgroundRemoval 183 5.3.1. PrincipleandAlgorithm 184 5.3.2. BackgroundRemoval 185 5.3.3. BaselineCorrection 191 5.3.4. BackgroundRemovalUsing ContinuousWaveletTransform 191 5.3.5. BackgroundRemovalof Two-DimensionalSignals 196 ✐ ✐ ✐ ✐ ✐ ✐ \ftoc" | 2004/1/28 | 10:10 | page ix | #5 ✐ ✐ contents ix 5.4. ResolutionEnhancement 199 5.4.1. NumericalDifferentiationUsing DiscreteWaveletTransform 200 5.4.2. NumericalDifferentiationUsing ContinuousWaveletTransform 205 5.4.3. ComparisonbetweenWavelet TransformandotherNumerical DifferentiationMethods 210 5.4.4. ResolutionEnhancement 212 5.4.5. ResolutionEnhancementbyUsing WaveletPacketTransform 220 5.4.6. ComparisonbetweenWavelet TransformandFastFourierTransform forResolutionEnhancement 221 5.5. CombinedTechniques 225 5.5.1. CombinedMethodforRegressionand Calibration 225 5.5.2. CombinedMethodforClassification andPatternRecognition 227 5.5.3. CombinedMethodofWavelet TransformandChemicalFactor Analysis 228 5.5.4. WaveletNeuralNetwork 230 5.6. AnOverviewoftheApplicationsinChemistry 232 5.6.1. FlowInjectionAnalysis 233 5.6.2. ChromatographyandCapillary Electrophoresis 234 5.6.3. Spectroscopy 238 5.6.4. Electrochemistry 244 5.6.5. MassSpectrometry 246 5.6.6. ChemicalPhysicsandQuantum Chemistry 248 5.6.7. Conclusion 249 APPENDIX VECTORANDMATRIXOPERATIONS ANDELEMENTARYMATLAB 257 A.1. ElementaryKnowledgeinLinearAlgebra 257 ✐ ✐ ✐ ✐ ✐ ✐ \ftoc" | 2004/1/28 | 10:10 | page x | #6 ✐ ✐ x contents A.1.1. VectorsandMatricesinAnalytical Chemistry 257 A.1.2. ColumnandRowVectors 259 A.1.3. AdditionandSubtractionofVectors 259 A.1.4. VectorDirectionandLength 260 A.1.5. ScalarMultiplicationofVectors 261 A.1.6. InnerandOuterProductsbetween Vectors 262 A.1.7. TheMatrixandItsOperations 263 A.1.8. MatrixAdditionandSubtraction 264 A.1.9. MatrixMultiplication 264 A.1.10. ZeroMatrixandIdentityMatrix 264 A.1.11. TransposeofaMatrix 265 A.1.12. DeterminantofaMatrix 265 A.1.13. InverseofaMatrix 266 A.1.14. OrthogonalMatrix 266 A.1.15. TraceofaSquareMatrix 267 A.1.16. RankofaMatrix 268 A.1.17. EigenvaluesandEigenvectorsofa Matrix 268 A.1.18. Singular-ValueDecomposition 269 A.1.19. GeneralizedInverse 270 A.1.20. DerivativeofaMatrix 271 A.1.21. DerivativeofaFunctionwith VectorasVariable 271 A.2. ElementaryKnowledgeofMATLAB 273 A.2.1. MatrixConstruction 275 A.2.2. MatrixManipulation 275 A.2.3. BasicMathematicalFunctions 276 A.2.4. MethodsforGeneratingVectors andMatrices 278 A.2.5. MatrixSubscriptSystem 280 A.2.6. MatrixDecomposition 286 A.2.6.1. Singular-Value Decomposition(SVD) 286 ✐ ✐ ✐ ✐