# Wavelets and Dilation Equations: A Brief Introduction

@article{Strang1989WaveletsAD, title={Wavelets and Dilation Equations: A Brief Introduction}, author={Gilbert Strang}, journal={SIAM Rev.}, year={1989}, volume={31}, pages={614-627} }

Wavelets are new families of basis functions that yield the representation $f(x) = \sum {b_{jk} W(2^j x - k)} $. Their construction begins with the solution $\phi (x)$ to a dilation equation with coefficients $c_k $. Then W comes from $\phi $, and the basis comes by translation and dilation of W. It is shown in Part 1 how conditions on the $c_k $ lead to approximation properties and orthogonality properties of the wavelets. Part 2 describes the recursive algorithms (also based on the $c_k…

## 1,091 Citations

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