Lifting for Filter Banks and Wavelets
Sean A Broughton, Kurt M. Bryan · 2018
This chapter focuses solely on signals, and develops lifting schemes for filter banks that act on such signals. It begins with a careful examination of the Haar filter bank, but from a point of view amenable to a lifting implementation. The chapter provides a detailed examination of lifting and polyphase matrix factorization, as well as topics such as filter bank design and integer-to-integer transforms. Before generalizing the polyphase analysis for the Haar transform, it will be helpful to develop a bit more material on Laurent polynomials and show how new perfect reconstruction filter banks can be obtained from existing filters via a process called “lifting”. The Matlab Wavelet Toolbox has built-in data structures and routines for handling Laurent polynomials. The chapter focuses on the construction and lifting factorization of the polyphase matrices for some standard filter banks, in particular, the CDF(2,2) and Daubechies D4 filter banks.