Algorithms for Daubechies Wavelets

  • Yves Nievergelt

Abstract

This chapter presents algorithms to calculate transforms with wavelets introduced by Ingrid Daubechies. In contrast to Haar’s simple-step wavelets, which exhibit jump discontinuities, Daubechies wavelets are continuous. As a consequence of their continuity, Daubechies wavelets approximate continuous signals more accurately with fewer wavelets than do Haar’s wavelets, but at the cost of intricate algorithms based upon a sophisticated theory. Therefore, to ease the transition from Haar wavelets to Daubechies wavelets, the present material postpones to a subsequent chapter the theoretical considerations that led to such wavelets, and focuses first upon a description of algorithms to calculate the Daubechies wavelet transform. Some logical derivations involve matrix algebra.

Keywords

Convolution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Yves Nievergelt
    • 1
  1. 1.Department of MathematicsEastern Washington UniversityCheneyUSA

Personalised recommendations