Algorithms for Daubechies Wavelets

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.