Algorithms for Daubechies Wavelets
Yves Nievergelt · Birkhäuser Boston eBooks · 1999
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. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.