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. The first part, concentrating on theoretical aspects, is written in a tutorial-like manner, with simple numerical examples. For the reader's convenience, all basic terms are explained in detail and all unique properties of wavelets are pinpointed and compared with the other types of basis function. The second part presents applications of wavelets from many branches of chemistry which will stimulate chemists to further exploration of this exciting subject.
Author(s): Beata Walczak (Eds.)
Series: Data Handling in Science and Technology 22
Edition: 1
Publisher: Elsevier Science
Year: 2000
Language: English
Pages: 3-554
Content:
Preface
Pages v-vi
Beata Walczak
List of contributors
Pages xv-xvi
Chapter 1 Finding frequencies in signals: The fourier transform Original Research Article
Pages 3-31
Bas van den Bogaert
Chapter 2 When frequencies change in time; towards the wavelet transform Original Research Article
Pages 33-55
Bas van den Bogaert
Chapter 3 Fundamentals of wavelet transforms Original Research Article
Pages 57-84
Y. Mallet, O. de Vel, D. Coomans
Chapter 4 The discrete wavelet transform in practice Original Research Article
Pages 85-118
O. de Vel, Y. Mallet, D. Coomans
Chapter 5 Multiscale methods for denoising and compression Original Research Article
Pages 119-150
Mohamed N. Nounou, Bhavik R. Bakshi
Chapter 6 Wavelet packet transforms and best basis algorithms Original Research Article
Pages 151-164
Y. Mallet, D. Coomans, O. de Vel
Chapter 7 Joint Basis and Joint best-basis for data sets Original Research Article
Pages 165-176
B. Walczak, D.L. Massart
Chapter 8 The adaptive wavelet algorithm for designing task specific wavelets Original Research Article
Pages 177-201
Y. Mallet, D. Coomans, O. de Vel
Chapter 9 Application of wavelet transform in processing chromatographic data Original Research Article
Pages 205-223
Foo-tim Chau, Alexander Kai-man Leung
Chapter 10 Application of wavelet transform in electrochemical studies Original Research Article
Pages 225-239
Foo-tim Chau, Alexander Kai-man Leung
Chapter 11 Applications of wavelet transform in spectroscopic studies 0110 0229 Original Research Article
Pages 241-261
Foo-tim Chau, Alexander Kai-man Leung
Chapter 12 Applications of wavelet analysis to physical chemistry Original Research Article
Pages 263-289
Heshel Teitelbaum
Chapter 13 Wavelet bases for IR library compression, searching and reconstruction Original Research Article
Pages 291-310
Beata Walczak, Jan P. Radomski
Chapter 14 Application of the discrete wavelet transformation for online detection of transitions in time series Original Research Article
Pages 311-321
M. Marth
Chapter 15 Calibration in wavelet domain Original Research Article
Pages 323-349
B. Walczak, D.L. Massart
Chapter 16 Wavelets in parsimonious functional data analysis models Original Research Article
Pages 351-410
Bjørn K. Alsberg
Chapter 17 Multiscale statistical process control and model-based 0144 0114 denoising Original Research Article
Pages 411-436
Bhavik R. Bakshi
Chapter 18 Application of adaptive wavelets in classification 0144 0114 and regression Original Research Article
Pages 437-456
Y. Mallet, D. Coomans, O. de Vel
Chapter 19 Wavelet-based image compression Original Research Article
Pages 457-478
O. de Vel, D. Coomans, Y. Mallett
Chapter 20 Wavelet analysis and processing of 2-D and 3-D analytical images Original Research Article
Pages 479-550
S.G. Nikolov, M. Wolkenstein, H. Hutter
Index
Pages 551-554
