Wavelets: Theory, Applications, Implementation

Mathematical Symbols and Notations / Introduction / Fundamental Concepts of Wavelets Transform / The Method of Wavelet Transform / Wavelets and Fractals / Wavelets and Functional Analysis / Discretization / Applications / Wavelets in Mathematical Physics / Conclusion / Index

Wavelet analysis has been at the centre stage of applied mathematics over the last two decades. It is the preferable alternative to Fourier analysis in signal processing when the signals are random and comprised of fluctuations of different scales. The beauty of wavelets reveals itself when applied to fractals or self-similar objects. This book aims at presenting a deductive scheme to show where and when the scale-invariance of Nature meets the representations of the affine group. It includes standard trends in wavelet analysis and discrete wavelet transform, some results obtained by the author in collaboration with different people in data processing, and a number of C++ programs which can be used by physicists, economists or biologists for the analysis of the time series. The general mathematical and physical ideas of wavelets are presented without sinking into details of elaborate numeric schems; at the same time it enables the reader to solve wavelet-related problems on the computer. The book also contains some new ideas developed by the author for non-standard applications of wavelets in quantum mechanics, quantum field theory and biology.