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.
... Wavelet Bases 217 4 . Wavelet - Galerkin Method 228 5 . Two - Scale Methods 248 6 . The Laplace Transform Wavelet Methods 256 7 . Discussion 266 8 . Conclusions 266 9 . References 269 VIII A PARALLEL TWO - DIMENSIONAL WAVELET PACKET ...
Meyer Wavelet As mentioned in the rest of Section 4.1.2, one can construct a wavelet function in the Fourier transform. The Meyer wavelet function ψ(x) is the first example of a wavelet function given its Fourier transform, ...
This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing.
Journal of Business, 45,444–455. Black, F. and Scholes, ... Fourier Analysis of Time Series: An Introduction, Second Edition. ... edition. Brock, W. A. (1986). Distinguishing random and deterministic systems: Abridged version.
In this fourth volume in the renown WAVELET ANALYSIS AND ITS APPLICATIONS Series, Efi Foufoula-Georgiou and Praveen Kumar begin with a self-contained overview of the nature, power, and scope of wavelet transforms.
In this book, the authors report the results obtained by the application of wavelet analysis to two physics experiments: the motion of variable mass pendulum and the motion of variable length pendulum.
This book presents the state of integration of wavelet theory and multiresolution analysis into soft computing. It is the first book on hybrid methods combining wavelet analysis with fuzzy logic, neural networks or genetic algorithms.
FROM REVIEWS OF THE SERIES "Reviews in Computational Chemistry remains the most valuable reference to methods and techniques in computational chemistry.
This book deals with statistical applications, especially wavelet based smoothing. The methods described in this text are examples of non-linear and non parametric curve fitting.
... wavelet transform in spectroscopic studies. In: Wavelets in Chemistry; vol.22; Walczak, B., Ed., Elsevier. Amsterdam, The Netherlands, pp. 241-261. 31. Teitelbaum, H., (2000). Application of wavelet analysis to physical chemistry. In: ...