Category: Science

Wavelet Applications in Chemical Engineering*Book Title:*9781461527084*ISBN 13:*1461527082*ISBN 10:*Rodolphe L. Motard, Babu Joseph*Author:*Science*Category:*Science*Category (general):*Springer Science & Business Media*Publisher:*323 pages, book*Format & Number of pages:*Other Public Domain Wavelet Software A number of public domain wavelet transform software are available for non-commercial, research, and educational purposes. Commercial software have been developed by the group at Yale and ...*Synopsis:*

Author. Date: 29 Mar 2010, Views:

Wavelets in Chemistry

Publisher: Elsevier Science | ISBN: 0444501118 | edition 2000 | File type: PDF | 572 pages | 23,1 mb

Wavelets seem to be the most efficient tool in signal denoising and compression. They can be used in an unlimited number of applications in all fields of chemistry where the instrumental signals are the source of information about the studied chemical systems or phenomena, and in all cases where these signals have to be archived. The quality of the instrumental signals determines the quality of answer to the basic analytical questions: how many components are in the studied systems, what are these components like and what are their concentrations? Efficient compression of the signal sets can drastically speed up further processing such as data visualization, modelling (calibration and pattern recognition) and library search. Exploration of the possible applications of wavelets in analytical chemistry has just started and this book will significantly speed up the process.

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Increasing emphasis on safety, productivity and quality control has provided an impetus to research on better methodologies for fault diagnosis, modeling, identification, control and optimization ofchemical process systems. One of the biggest challenges facing the research community is the processing of raw sensordata into meaningful information. Wavelet analysis is an emerging field of mathematics that has provided new tools and algorithms suited for the type of problems encountered in process monitoring and control. The concept emerged in the geophysical field as a result ofthe need for time-frequency analytical techniques. It has since been picked up by mathematicians and recognized as a unifying theory for many ofthe methodologies employed in the past in physics and signal processing. l Meyer states: "Wavelets are without doubt an exciting and intuitive concept. The concept brings with it a new way of thinking, which is absolutely essential and was entirely missing in previously existing algorithms. " The unification ofthe theory from these disciplines has led to applications of wavelet transforms in many areas ofscience and engineering including: • pattern recognition • signal analysis • time-frequency decomposition • process signal characterization and representation • process system modeling and identification • control system design, analysis and implementation • numerical solution ofdifferential equations • matrix manipulation About a year ago, in talking to various colleagues and co-workers, it became clear that a number of chemical engineers were fascinated with this new concept.

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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.

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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.

*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.

2.2.3.1. Discrete Fourier Transformation and Spectral Multiplex Advantage.

2.2.3.2. Fast Fourier Transformation.

2.2.3.3. Fourier Transformation as Applied to Smooth Analytical Signals.

2.2.3.4. 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.

3.6.2.1. Evolving Factor Analysis (EFA).

3.6.2.2. Window Factor Analysis (WFA).

3.6.2.3. 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

*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.

"Statisticians, biochemists, engineers, and health researchers will benefit a lot from this wonderful book." (*Journal of Statistical Computation and Simulation*. November 2005)

". quite useful for persons who apply signal processing methods in chemistry." (*Technometrics*. May 2005)

"…my overall impression of the text is favorable…I would recommend this book to chemists who are interested in using wavelets in their research and to faculty…" (*Journal of the American Chemical Society*. February 23, 2005)

"I recommend this book to chemists who are interested in using wavelets in their research and to faculty who would like to teach graduate students about signal processing. " (*Analytical Chemistry*. February 1, 2005)

"The presentation of information makes it easy for reader to find the relevant information. The text is well-written and understandable." (*E-STREAMS*. October 2004)

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Seeking to capture the essence of the current state of research in wavelet analysis and its applications, this text identifies the changes and opportunities – both current and future – in the field.

The papers are taken from the Third International Conference on Wavelet Analysis and Its Applications, held in Chongqing, China, in 2003. Researchers such as Professor John Daugman from Cambridge University and Professor Victor Wickerhauser from Washington University present their research papers.

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