The Fast Lifting Wavelet Transform

This tutorial is a sequel to the wavelet tutorial, which will fill in the blank spots on the wavelet transform map, add some detail and even explore the area outside it. We start with taking a closer look at the scaling and wavelet filters in general, what they should look like, what their constraints are and how they can be used in the inverse wavelet transform. Then we will do some algebra and develop a general framework to design filters for every possible wavelet transform. Using the lifting scheme we will in the end arrive at a universal discrete wavelet transform which yields only integer wavelet- and scaling coefficients instead of the usual floating point coefficients. In order to clarify the theory in this tutorial a detailed example will be presented.