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Other titles in the Chemical Analysis series:
Chemometricsby Foo-tim (edt) Chau
Synopses & Reviews
All the tools chemists need to analyze chemical data and produce more useful information
The statistical and mathematical methods of chemometrics present a wide array of modeling and processing tools for maximizing useful information from experimental data. These methods both reduce time spent in the laboratory and allow researchers to extract more information from data collected. However, understanding the advanced mathematical background of the latest of these approaches, as well as how to apply them, can still be a time-consuming endeavor for the working chemist.
Chemometrics: From Basics to Wavelet Transform provides a one-stop resource for comprehending the range of available chemometric methods, from basic principles to the theory and practice of wavelet transform. Covering the background of chemometrics, common signal processing techniques, and applications in analytical chemistry, this helpful guide also features:
Throughout Chemometrics, the emphasis remains on giving practitioners a useful summary of the latest methods and their real-world applications. Right up to the most modern innovations of wavelet transform, Chemometrics combines timeliness with accessibility to offer chemists, biochemists, and advanced students a vital reference volume.
Book News Annotation:
Chau (Department of Applied Biology and Chemical Technology, Hong Kong Polytechnic University) provides a resource for understanding the range of available chemometric methods, from basic principles to the theory and practice of wavelet transforms, in this reference for working chemists. Covering the mathematical background of chemometrics, common signal processing techniques, and applications in analytical chemistry, the book features simple language and illustrative examples, reviews of other methods in comparison to wavelet techniques, and a companion FTP site with MATLAB code and data sets. Emphasis is on the latest methods and real-world applications.
Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)
Intended Audience: Professionals and students working in analytical chemistry and process chemistry, as well as physical chemistry, spectroscopy, and statistics.
Wavelet Transformations and Their Applications in Chemistry pioneers a new approach to classifying existing chemometric techniques for data analysis in one and two dimensions, using a practical applications approach to illustrating chemical examples and problems. Written in a simple, balanced, applications-based style, the book is geared to both theorists and non-mathematicians.
This text emphasizes practical applications in chemistry. It employs straightforward language and examples to show the power of wavelet transforms without overwhelming mathematics, reviews other methods, and compares wavelets with other techniques that provide similar capabilities. It uses examples illustrated in MATLAB codes to assist chemists in developing applications, and includes access to a supplementary Web site providing code and data sets for work examples. Wavelet Transformations and Their Applications in Chemistry will prove essential to professionals and students working in analytical chemistry and process chemistry, as well as physical chemistry, spectroscopy, and statistics.
About the Author
FOO-TIM CHAU, PhD, is a Professor in the Department of Applied Biology and Chemical Technology at Hong Kong Polytechnic University.
YI-ZENG LIANG, PhD, is a Professor in the College of Chemistry and Chemical Engineering at Central South University, China.
JUNBIN GAO, PhD, is a Professor in the Department of Mathematics at Huazhong University of Science and Technology. He is currently visiting the University of Southhampton.
XUE-GUANG SHAO, PhD, is a Professor at the University of Science and Technology in China.
Table of Contents
CHAPTER 1: INTRODUCTION.
1.1. Modern Analytical Chemistry.
1.1.1. Developments in Modern Chemistry.
1.1.2. Modern Analytical Chemistry.
1.1.3. Multidimensional Dataset.
1.2.1. Introduction to Chemometrics.
1.2.2. Instrumental Response and Data Processing.
1.2.3. White, Black, and Gray Systems.
1.3. Chemometrics-Based Signal Processing Techniques.
1.3.1. Common Methods for Processing Chemical Data.
1.3.2. Wavelets in Chemistry.
1.4. Resources Available on Chemometrics and Wavelet Transform.
1.4.2. Online Resources.
1.4.3. Mathematics Software.
CHAPTER 2: ONE-DIMENSIONAL SIGNAL PROCESSING TECHNIQUES IN CHEMISTRY.
2.1. Digital Smoothing and Filtering Methods.
2.1.1. Moving-Window Average Smoothing Method.
2.1.2. Savitsky--Golay Filter.
2.1.3. Kalman Filtering.
2.1.4. Spline Smoothing.
2.2. Transformation Methods of Analytical Signals.
2.2.1. Physical Meaning of the Convolution Algorithm.
2.2.2. Multichannel Advantage in Spectroscopy and Hadamard Transformation.
2.2.3. Fourier Transformation.
126.96.36.199. Discrete Fourier Transformation and Spectral Multiplex Advantage.
188.8.131.52. Fast Fourier Transformation.
184.108.40.206. Fourier Transformation as Applied to Smooth Analytical Signals.
220.127.116.11. Fourier Transformation as Applied to Convolution and Deconvolution.
2.3. Numerical Differentiation.
2.3.1. Simple Difference Method.
2.3.2. Moving-Window Polynomial Least-Squares Fitting Method.
2.4. Data Compression.
2.4.1. Data Compression Based on B-Spline Curve Fitting.
2.4.2. Data Compression Based on Fourier Transformation.
2.4.3. Data Compression Based on Principal-Component Analysis.
CHAPTER 3: TWO-DIMENSIONAL SIGNAL PROCESSING TECHNIQUES IN CHEMISTRY.
3.1. General Features of Two-Dimensional Data.
3.2. Some Basic Concepts for Two-Dimensional Data from Hyphenated Instrumentation.
3.2.1. Chemical Rank and Principal-Component Analysis (PCA).
3.2.2. Zero-Component Regions and Estimation of Noise Level and Background.
3.3. Double-Centering Technique for Background Correction.
3.4. Congruence Analysis and Least-Squares Fitting.
3.5. Differentiation Methods for Two-Dimensional Data.
3.6 Resolution Methods for Two-Dimensional Data.
3.6.1. Local Principal-Component Analysis and Rankmap.
3.6.2. Self-Modeling Curve Resolution and Evolving Resolution Methods.
18.104.22.168. Evolving Factor Analysis (EFA).
22.214.171.124. Window Factor Analysis (WFA).
126.96.36.199. Heuristic Evolving Latent Projections (HELP).
CHAPTER 4: FUNDAMENTALS OF WAVELET TRANSFORM.
4.1. Introduction to Wavelet Transform and Wavelet Packet Transform.
4.1.1. A Simple Example: Haar Wavelet.
4.1.2. Multiresolution Signal Decomposition.
4.1.3. Basic Properties of Wavelet Function.
4.2. Wavelet Function Examples.
4.2.1. Meyer Wavelet.
4.2.2. B-Spline (Battle—Lemarié) Wavelets.
4.2.3. Daubechies Wavelets.
4.2.4. Coiflet Functions.
4.3. Fast Wavelet Algorithm and Packet Algorithm.
4.3.1. Fast Wavelet Transform.
4.3.2. Inverse Fast Wavelet Transform.
4.3.3. Finite Discrete Signal Handling with Wavelet Transform.
4.3.4. Packet Wavelet Transform.
4.4. Biorthogonal Wavelet Transform.
4.4.1. Multiresolution Signal Decomposition of Biorthogonal Wavelet.
4.4.2. Biorthogonal Spline Wavelets.
4.4.3. A Computing Example.
4.5. Two-Dimensional Wavelet Transform.
4.5.1. Multidimensional Wavelet Analysis.
4.5.2. Implementation of Two-Dimensional Wavelet Transform.
CHAPTER 5: APPLICATION OF WAVELET TRANSFORM IN CHEMISTRY.
5.1. Data Compression.
5.1.1. Principle and Algorithm.
5.1.2. Data Compression Using Wavelet Packet Transform.
5.1.3. Best-Basis Selection and Criteria for Coefficient Selection.
5.2. Data Denoising and Smoothing.
5.2.3. Denoising and Smoothing Using Wavelet Packet Transform.
5.2.4. Comparison between Wavelet Transform and Conventional Methods.
5.3. Baseline/Background Removal.
5.3.1. Principle and Algorithm.
5.3.2. Background Removal.
5.3.3. Baseline Correction.
5.3.4. Background Removal Using Continuous Wavelet Transform.
5.3.5. Background Removal of Two-Dimensional Signals.
5.4. Resolution Enhancement.
5.4.1. Numerical Differentiation Using Discrete Wavelet Transform.
5.4.2. Numerical Differentiation Using Continuous Wavelet Transform.
5.4.3. Comparison between Wavelet Transform and other Numerical Differentiation Methods.
5.4.4. Resolution Enhancement.
5.4.5. Resolution Enhancement by Using Wavelet Packet Transform.
5.4.6. Comparison between Wavelet Transform and Fast Fourier Transform for Resolution Enhancement.
5.5. Combined Techniques.
5.5.1. Combined Method for Regression and Calibration.
5.5.2. Combined Method for Classification and Pattern Recognition.
5.5.3. Combined Method of Wavelet Transform and Chemical Factor Analysis.
5.5.4. Wavelet Neural Network.
5.6. An Overview of the Applications in Chemistry.
5.6.1. Flow Injection Analysis.
5.6.2. Chromatography and Capillary Electrophoresis.
5.6.5. Mass Spectrometry.
5.6.6. Chemical Physics and Quantum Chemistry.
APPENDIX VECTOR AND MATRIX OPERATIONS AND ELEMENTARY MATLAB.
A.1. Elementary Knowledge in Linear Algebra.
A.1.1. Vectors and Matrices in Analytical Chemistry.
A.1.2. Column and Row Vectors.
A.1.3. Addition and Subtraction of Vectors.
A.1.4. Vector Direction and Length.
A.1.5. Scalar Multiplication of Vectors.
A.1.6. Inner and Outer Products between Vectors.
A.1.7. The Matrix and Its Operations.
A.1.8. Matrix Addition and Subtraction.
A.1.9. Matrix Multiplication.
A.1.10. Zero Matrix and Identity Matrix.
A.1.11. Transpose of a Matrix.
A.1.12. Determinant of a Matrix.
A.1.13. Inverse of a Matrix.
A.1.14. Orthogonal Matrix.
A.1.15. Trace of a Square Matrix.
A.1.16. Rank of a Matrix.
A.1.17. Eigenvalues and Eigenvectors of a Matrix.
A.1.18. Singular-Value Decomposition.
A.1.19. Generalized Inverse.
A.1.20. Derivative of a Matrix.
A.1.21. Derivative of a Function with Vector as Variable.
A.2. Elementary Knowledge of MATLAB.
A.2.1. Matrix Construction.
A.2.2. Matrix Manipulation.
A.2.3. Basic Mathematical Functions.
A.2.4. Methods for Generating Vectors and Matrices.
A.2.5. Matrix Subscript System.
A.2.6. Matrix Decomposition.
A.2.6.1. Singular-Value Decomposition (SVD).
A.2.6.2. Eigenvalues and Eigenvectors (eig).
A.2.7. Graphic Functions 288
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