The Discrete Wavelet Transform with Lifting : A Step by Step Introduction
C Elofson · 2004
There is a great deal of information pertaining to wavelets readily available from various sources; several of the more recent sources describe the lifting technique for constructing wavelets. The tutorial paper by Sweldens and Schr{umlt o}der [1] gives a thorough explanation of the lifting approach for Haar bases. While it provides an excellent introduction to the topic, it is not immediately obvious how this approach is extended to nonuniformly spaced data on finite intervals. The present paper provides intermediate steps that supplement the material in [1]. After working through the following discussion, the reader should have no problem deriving the relevant equations presented in Sweldens and Schr{umlt o}der's article. Because of the abundance of information on the Haar basis, this discussion will instead work through the steps using a linear basis set.