Application of Wavelets in Chemistry

B. Walczak, B. van den Bogaert and D.L. Massart. Application of Wavelet Packet Transform in Pattern Recognition of NIR Data, Analytical Chemistry, 68 (1996) 1742-1747. 

J. Chen, H.B. Zhong, Z.X. Pan and M.S. Zhang, Application of wavelet transform in differential pulse voltammetric data processing, Chinese Journal of Analytical Chemistry, 24 (1996), 1002-1006 (in Chinese)... 

J.B. Zheng, H.B. Zhong, H.Q. Zhang and D.Y. Yang. Application of Wavelet Transform in Retrieval of Useful Information from d-E dt- —t Signal. Chinese Journal of Analytical Chemistry, 26 (1998), 25 28 (in Chinese). 

The application of wavelet analysis to physical chemistry and chemical physics is in its infancy. The present survey indicates that there are many opportunities remaining to advance the fields of quantum chemistry, chemical dynamics and chemical kinetics by using this powerful new tool. 

The application of wavelet transforms to the analysis of spectra and other chemical data has gained popularity in chemistry [22-30]. Examples of typical chemical signal processing application are ... 

Wavelet transforms are a quite new field of data processing, but they have proven to be a valuable addition to the analyst s collection of tools. Therefore, they should be introduced here a detailed discussion of how the transformation procedure is applied to descriptors can be found in the next chapter. A general overview of wavelet transformations is described by Strang [57] the mathematical details are published by DeVore and Lucier [58] and a review on applications in chemistry is given by Leung et al. [59]. 

Table 1. Number of published papers from 1989 to 1998 that relate to the application of the wavelet transform in chemistry.

Two special applications of WT to chromatographic studies have been reported in recent years. Collantes et al. [44] proposed the employment of the wavelet packets transform (WPT) for pre-processing HPLC results by an artificial neural network. The application of WPT for data processing in chemistry is very rare. These authors aimed to evaluate several artificial... 

L.J. Bao, J.Y. Mo and Z.Y. Tang. The Application in Processing Analytical Chemistry Signals of a Cardinal Spline Approach to Wavelets. Analytical Chemistry, 69 (1997), 3053-3057. 

L.J. Bao, Z.Y. Tang and J.Y. Mo, The Application of Spline Wavelet and Fourier Transform in Analytical Chemistry, In New Trends in Chemometrics, First International Conference on Chemometrics in China, Zhangjiajie, China, October 17-22, 1997, (Y.Z. Liang, R. Nortvedt, O.M. Kvalheim, H.L. Shen, Eds) Hunan University Press, Changsha, (1997), pp. 197-198. 

X.P. Zheng, J.Y. Mo and P.X. Cai, Simultaneous Application of Spline Wavelet and Riemann-Liouville Transform Filtration in Electroanalytical Chemistry, Analytical Communication, 35 (1998), 57-59. 

The book is written in the tutorial-like manner. We intended to gently introduce wavelets to an audience of chemists. Although the particular chapters are written by independent authors, we intended to cover all important aspects of wavelet theory and to present wavelet applications in chemistry and in chemical engineering. 

Basic concepts of wavelet theory, together with all important aspects of wavelet transforms, are presented in the first part of the book. This part is extensively illustrated with figures and simulated examples. The second part of this book consists of examples of wavelet applications in chemistry and in chemical engineering. 

This article will present a very brief sketch of the history and theory of wavelet analysis, and then list a few applications to physical and computational chemistry. The subject spans many disciplines, and its literature comprises thousands of articles and books, making it easy to venture beyond the current scope. The popular surveys in the bibliography are a good source of more general information the ambitious reader is invited to consult the more technical works for the mathematical details. Most applications to date are described in scholarly journals, but many are collected in edited compilations. " ... 

As stated previously, with most applications in analytical chemistry and chemometrics, the data we wish to transform are not continuous and infinite in size but discrete and finite. We cannot simply discretise the continuous wavelet transform equations to provide us with the lattice decomposition and reconstruction equations. Furthermore it is not possible to define a MRA for discrete data. One approach taken is similar to that of the continuous Fourier transform and its associated discrete Fourier series and discrete Fourier transform. That is, we can define a discrete wavelet series by using the fact that discrete data can be viewed as a sequence of weights of a set of continuous scaling functions. This can then be extended to defining a discrete wavelet transform (over a finite interval) by equating it to one period of the data length and generating a discrete wavelet series by its infinite periodic extension. This can be conveniently done in a matrix framework. 

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