# 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}
}
• G. Strang
• Published 1 December 1989
• Computer Science
• SIAM Rev.
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…
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