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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