Discrete Wavelets and Multiresolution Analysis
Henk J.A.M. Heijmans · WORLD SCIENTIFIC eBooks · 1993
In this paper we present an elementary discussion of the discrete wavelet transform.A major problem is formed by the construction of an orthonormal wavelet basis of the Hilbert space of square integrable functions.It is shown that the concept of a multiresolution analysis is very helpful to make such a construction.With every multiresolution analysis one can associate a father wavelet, the translates of which define an orthonormal system, and a mother wavelet which forms the basis for the discrete wavelet transform.This transform can be associated with two filtering operations and their adjoints; in practice these are used to get a pyramid-like decomposition of a signal.The abstract theory is illustrated by means of two concrete examples, the sine-wavelet and the Meyer-wavelet.