Titlebook: Wavelet Analysis; The Scalable Structu Howard L. Resnikoff,Raymond O. Wells Textbook 1998 Springer Science+Business Media New York 1998 Mod

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Examples of One-Dimensional Wavelet Systems scaling functions and wavelets that have helped the authors to understand wavelets and develop intuition about them. The classes of wavelets in the list below seem to us to capture many of the features that are important for applications or have a special signficance for the mathematical theory. So

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The Mallat Algorithm. for instance) in terms of an infinite orthonormal basis (or tight frame in the general case). For applications of this theory to real-world situations, it is necessary to deal with suitable finite-dimensional approximations of the functions being represented and the representing wavelet basis. If

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Examples of One-Dimensional Wavelet Systems scaling functions and wavelets that have helped the authors to understand wavelets and develop intuition about them. The classes of wavelets in the list below seem to us to capture many of the features that are important for applications or have a special signficance for the mathematical theory. So

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Higher-Dimensional Wavelet Systemsattice subgroup of ., . is a strictly expansive linear transformation with .Λ ⊂ Λ, and . = |det.|. The ., ψ., 1 ≤ . ≤ . −1 are defined by functional equations having the form . where . are complex-valued functions having finite support on Λ and satisfy certain algebraic conditions, and the . ϕ satis