What question did this study set out to answer?

To introduce wavelets and their construction through dilation equations and to highlight their approximation and orthogonality properties.

December 1, 1989SIAM Review

Wavelets and Dilation Equations: A Brief Introduction

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GSGilbert StrangUniversité Paris-Sud

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Implication

This brief introduction explores wavelets constructed from dilation equations and their properties, aiming for efficient localization in time and frequency.

Key Points

To introduce wavelets and their construction through dilation equations and to highlight their approximation and orthogonality properties.
Introduced wavelets as basis functions represented through a dilation equation with coefficients.
Described how translation and dilation of the basis lead to properties of wavelets.
Explained recursive algorithms used for decomposing and reconstructing functions.
Conditions on the coefficients $c_k$ lead to improved approximation properties of wavelets.
Wavelets demonstrate orthogonality properties essential for efficient function representation.
Algorithms for decomposition and reconstruction prove effective for localizing signals in time and frequency domains.

Cite This Study

Gilbert Strang (1989) studied this question.

synapsesocial.com/papers/6a0ea98ac1254035622296da https://doi.org/10.1137/1031128

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Implication

This brief introduction explores wavelets constructed from dilation equations and their properties, aiming for efficient localization in time and frequency.

Wavelets and Dilation Equations: A Brief Introduction

Discussion

Member takes

Implication

Key Points

Cite This Study

Wavelets and Dilation Equations: A Brief Introduction

Discussion

Member takes

Implication

Key Points

Cite This Study

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