Titlebook: Wavelets Made Easy; Yves Nievergelt Textbook 1999 Springer Science+Business Media New York 1999 Applications of Mathematics.Numerical Math

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Textbook 1999n after compression or other modification). Such applications include one-dimensional signals (sounds or other time-series), two-dimensional arrays (pictures or maps), and three-dimensional data (spatial diffusion). The ap- plications demonstrated here do not constitute recipes for real implementati

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onstruction after compression or other modification). Such applications include one-dimensional signals (sounds or other time-series), two-dimensional arrays (pictures or maps), and three-dimensional data (spatial diffusion). The ap- plications demonstrated here do not constitute recipes for real implementati978-1-4612-6823-9978-1-4612-0573-9

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Daubechies Wavelets DesignUsing the example of Daubechies wavelets, this chapter demonstrates how to use the Fourier transform to investigate the existence, the uniqueness, and the design of recursive, mutually orthogonal, compactly supported, and continuous wavelets.

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Fourier Series for Periodic FunctionsThis chapter introduces a few features of Fourier series. In contrast to the Discrete Fourier Transform, which pertains to finite-dimensional spaces, Fourier series provide an approach to the concept of approximation of functions in linear spaces that do not admit finite bases, in a context simpler than that of Daubechies wavelets.

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Signal Representations with WaveletsUsing the example of Daubechies wavelets, this chapter demonstrates how to investigate the accuracy with which recursive, mutually orthogonal, compactly supported, and continuous wavelets can represent signals (mathematical functions).

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