Chemometrics wavelet transform

Chemometrics From Basics to Wavelet Transform. By Foo-tim Chau, Yi-Zeng Liang,... 

Sample Preparation Techniques in Analytical Chemistry. Edited by Somenath Mitra Analysis and Purification Methods in Combination Chemistry. Edited by Bing Yan Chemometrics From Basics to Wavelet Transform. By Foo-tim Chau, Yi-Zeng Liang, Junbin Gao, and Xue-guang Shao... 

Also, we do not cover several typical chemometrics types of analyses, such as cluster analysis, experimental design, pattern recognition, classification, neural networks, wavelet transforms, qualimetrics etc. This explains our decision not to include the word chemometrics in the title. 

Generally, chemometrics handles data sets constituted by many objects described by the same variables. In this perspective, the application of wavelet transform should be performed, obtaining, for all the objects, a single basis formed by the same coefficients, the so-called common best basis. 

Depezynski, U., Jetter, K., Molt, K and Niemoller, A. (1997) The fast wavelet transform on compact intervals as a tool in chemometrics. I. Mathematical background. Chemom. Intell. Lab. Syst., 39, 19-27. 

Principles and applications of wavelet transformation to chemometrics. Anal. Chim. Acta, 420, 169-180. 

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. 

B.K. Alsberg, A.M. Woodward and D.B. Kell, An Introduction to Wavelet Transforms for Chemometricians A Time-frequency Approach. Chemometrics Intelligent Laboratory Systems 37 (1997). 215-239. 

X.G. Shao, W.S. Cai and P.Y. Sun, Determination of the Component Number in Overlapping Multicomponent Chromatogram using Wavelet Transform, Chemometrics Intelligent Laboratory Systems 43 (1998), 147-155. 

A.K.M. Leung, F.T. Chau and J.B. Gao, A Review on Applications of Wavelet Transform Techniques in Chemical Analysis 1989-1997, Chemometric and Intelligence Laboratory Systems. 43 (1998), 165-184. 

U. Depczynski, K. Jetter, K. Molt and A. Niemoller, The Fast Wavelet Transform on Compact Intervals as a Tool in Chemometrics. 1. Mathematical Background, Chemometrics and Intelligent Laboratory Systems, 39 (1997), 19-27. 

Akay, M. Time Frequency and wavelets. In Akay, M. (ed.) Biomedical Signal Processing IEEE Press Series in Biomedical Engineering. Wiley—IEEE Press, Piscataway (1997) Alsberg, B.K., Woodward, A.M., Kell, D.B. An introduction to wavelet transform for chemometricians a time-frequency approach. Chemometr. Intell. Lab. Syst. 37, 215-239... 

The Fast Wavelet Transform on Compact Intervals as a Tool in Chemometrics. I. Mathematical Bacl ound. 

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. 

B. Walczak and D.L. Massart, Noise supression and signal compression using wavelet packet transform, Chemometrics ami Intelligent Laboratory Systems 36 (1997), 81-94. 

---