Chemometrics: from basics to wavelet transform

Chemometrics......Page 4
CONTENTS......Page 8
PREFACE......Page 16
1.1.1. Developments in Modern Chemistry......Page 18
1.1.2. Modern Analytical Chemistry......Page 19
1.1.3. Multidimensional Dataset......Page 20
1.2.1. Introduction to Chemometrics......Page 22
1.2.2. Instrumental Response and Data Processing......Page 25
1.2.3. White, Black, and Gray Systems......Page 26
1.3.1. Common Methods for Processing Chemical Data......Page 27
1.3.2. Wavelets in Chemistry......Page 28
1.4.1. Books......Page 29
1.4.2. Online Resources......Page 31
1.4.3. Mathematics Software......Page 32
2.1. Digital Smoothing and Filtering Methods......Page 40
2.1.1. Moving-Window Average Smoothing Method......Page 41
2.1.2. Savitsky-Golay Filter......Page 42
2.1.3. Kalman Filtering......Page 49
2.1.4. Spline Smoothing......Page 53
2.2.1. Physical Meaning of the Convolution Algorithm......Page 56
2.2.2. Multichannel Advantage in Spectroscopy and Hadamard Transformation......Page 58
2.2.3. Fourier Transformation......Page 61
2.2.3.1. Discrete Fourier Transformation and Spectral Multiplex Advantage......Page 62
2.2.3.2. Fast Fourier Transformation......Page 65
2.2.3.3. Fourier Transformation as Applied to Smooth Analytical Signals......Page 67
2.2.3.4. Fourier Transformation as Applied to Convolution and Deconvolution......Page 69
2.3.1. Simple Difference Method......Page 71
2.3.2. Moving-Window Polynomial Least-Squares Fitting Method......Page 72
2.4.1. Data Compression Based on B-Spline Curve Fitting......Page 74
2.4.3. Data Compression Based on Principal-Component Analysis......Page 81
3.1. General Features of Two-Dimensional Data......Page 86
3.2. Some Basic Concepts for Two-Dimensional Data from Hyphenated Instrumentation......Page 87
3.2.1. Chemical Rank and Principal-Component Analysis (PCA)......Page 88
3.2.2. Zero-Component Regions and Estimation of Noise Level and Background......Page 92
3.3. Double-Centering Technique for Background Correction......Page 94
3.4. Congruence Analysis and Least-Squares Fitting......Page 95
3.5. Differentiation Methods for Two-Dimensional Data......Page 97
3.6 Resolution Methods for Two-Dimensional Data......Page 98
3.6.1. Local Principal-Component Analysis and Rankmap......Page 100
3.6.2. Self-Modeling Curve Resolution and Evolving Resolution Methods......Page 102
3.6.2.1. Evolving Factor Analysis (EFA)......Page 105
3.6.2.2. Window Factor Analysis (WFA)......Page 107
3.6.2.3. Heuristic Evolving Latent Projections (HELP)......Page 111
CHAPTER 4 FUNDAMENTALS OF WAVELET TRANSFORM......Page 116
4.1. Introduction to Wavelet Transform and Wavelet Packet Transform......Page 117
4.1.1. A Simple Example: Haar Wavelet......Page 120
4.1.2. Multiresolution Signal Decomposition......Page 125
4.1.3. Basic Properties of Wavelet Function......Page 129
4.2.1. Meyer Wavelet......Page 130
4.2.2. B-Spline (Battle-Lemarié) Wavelets......Page 131
4.2.3. Daubechies Wavelets......Page 133
4.2.4. Coiflet Functions......Page 134
4.3. Fast Wavelet Algorithm and Packet Algorithm......Page 135
4.3.1. Fast Wavelet Transform......Page 136
4.3.2. Inverse Fast Wavelet Transform......Page 139
4.3.3. Finite Discrete Signal Handling with Wavelet Transform......Page 142
4.3.4. Packet Wavelet Transform......Page 149
4.4.1. Multiresolution Signal Decomposition of Biorthogonal Wavelet......Page 151
4.4.2. Biorthogonal Spline Wavelets......Page 153
4.4.3. A Computing Example......Page 154
4.5.1. Multidimensional Wavelet Analysis......Page 157
4.5.2. Implementation of Two-Dimensional Wavelet Transform......Page 158
CHAPTER 5 APPLICATION OF WAVELET TRANSFORM IN CHEMISTRY......Page 164
5.1. Data Compression......Page 165
5.1.1. Principle and Algorithm......Page 166
5.1.2. Data Compression Using Wavelet Packet Transform......Page 172
5.1.3. Best-Basis Selection and Criteria for Coefficient Selection......Page 175
5.2. Data Denoising and Smoothing......Page 183
5.2.1. Denoising......Page 184
5.2.2. Smoothing......Page 190
5.2.3. Denoising and Smoothing Using Wavelet Packet Transform......Page 196
5.2.4. Comparison between Wavelet Transform and Conventional Methods......Page 199
5.3. Baseline/Background Removal......Page 200
5.3.1. Principle and Algorithm......Page 201
5.3.2. Background Removal......Page 202
5.3.4. Background Removal Using Continuous Wavelet Transform......Page 208
5.3.5. Background Removal of Two-Dimensional Signals......Page 213
5.4. Resolution Enhancement......Page 216
5.4.1. Numerical Differentiation Using Discrete Wavelet Transform......Page 217
5.4.2. Numerical Differentiation Using Continuous Wavelet Transform......Page 222
5.4.3. Comparison between Wavelet Transform and other Numerical Differentiation Methods......Page 227
5.4.4. Resolution Enhancement......Page 229
5.4.5. Resolution Enhancement by Using Wavelet Packet Transform......Page 237
5.4.6. Comparison between Wavelet Transform and Fast Fourier Transform for Resolution Enhancement......Page 238
5.5.1. Combined Method for Regression and Calibration......Page 242
5.5.2. Combined Method for Classification and Pattern Recognition......Page 244
5.5.3. Combined Method of Wavelet Transform and Chemical Factor Analysis......Page 245
5.5.4. Wavelet Neural Network......Page 247
5.6. An Overview of the Applications in Chemistry......Page 249
5.6.1. Flow Injection Analysis......Page 250
5.6.2. Chromatography and Capillary Electrophoresis......Page 251
5.6.3. Spectroscopy......Page 255
5.6.4. Electrochemistry......Page 261
5.6.5. Mass Spectrometry......Page 263
5.6.6. Chemical Physics and Quantum Chemistry......Page 265
5.6.7. Conclusion......Page 266
A.1.1. Vectors and Matrices in Analytical Chemistry......Page 274
A.1.3. Addition and Subtraction of Vectors......Page 276
A.1.4. Vector Direction and Length......Page 277
A.1.5. Scalar Multiplication of Vectors......Page 278
A.1.6. Inner and Outer Products between Vectors......Page 279
A.1.7. The Matrix and Its Operations......Page 280
A.1.10. Zero Matrix and Identity Matrix......Page 281
A.1.12. Determinant of a Matrix......Page 282
A.1.14. Orthogonal Matrix......Page 283
A.1.15. Trace of a Square Matrix......Page 284
A.1.17. Eigenvalues and Eigenvectors of a Matrix......Page 285
A.1.18. Singular-Value Decomposition......Page 286
A.1.19. Generalized Inverse......Page 287
A.1.21. Derivative of a Function with Vector as Variable......Page 288
A.2. Elementary Knowledge of MATLAB......Page 290
A.2.2. Matrix Manipulation......Page 292
A.2.3. Basic Mathematical Functions......Page 293
A.2.4. Methods for Generating Vectors and Matrices......Page 295
A.2.5. Matrix Subscript System......Page 297
A.2.6.1. Singular-Value Decomposition (SVD)......Page 303
A.2.6.2. Eigenvalues and Eigenvectors (eig)......Page 304
A.2.7. Graphic Functions......Page 305
INDEX......Page 310