Multiresolution approximations and wavelet orthonormal bases of L^2(R)
TLDR
In this paper, the authors study the properties of multiresolution approximation and prove that it is characterized by a 2π periodic function, which is further described in terms of wavelet orthonormal bases.Abstract:
A multiresolution approximation is a sequence of embedded vector spaces V j jmember Z for approximating L 2 (R) functions. We study the properties of a multiresolution approximation and prove that it is characterized by a 2π periodic function which is further described. From any multiresolution approximation, we can derive a function ψ(x) called a wavelet such that √ 2 j ψ(2 j x −k) (k ,j)member Z 2 is an orthonormal basis of L 2 (R). This provides a new approach for understanding and computing wavelet orthonormal bases. Finally, we characterize the asymptotic decay rate of multiresolution approximation errors for functions in a Sobolev space H s .read more
Citations
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Proceedings ArticleDOI
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Riesz wavelets and multiresolution structures
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Wavelet Neural Modeling for Hydrologic Time Series Forecasting with Uncertainty Evaluation
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Shearlet Multiresolution and Multiple Refinement
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Spectral characteristic of geomagnetically induced current during geomagnetic storms by wavelet techniques
Binod Adhikari,Binod Adhikari,Nirakar Sapkota,Subodh Dahal,Binod Bhattarai,Krishna Khanal,Narayan P. Chapagain +6 more
TL;DR: In this article, the authors explored the remarkable ability of wavelets to highlight the singularities associated with discontinuities present in the GIC signal associated with four geomagnetic storms and found distinct periodicities at the time when H component highly perturbed.
References
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Exact reconstruction techniques for tree-structured subband coders
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Journal ArticleDOI
Analysis of sound patterns through wavelet transforms
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