ABSTRACT
This chapter discusses an important method of construction of wavelets of arbitrary smoothness. It explores a rich arsenal of functions giving rise to wavelets, namely spline functions and explores two important classes of compactly supported wavelet bases, namely the compactly supported orthonormal and the biorthogonal wavelet bases. These wavelet bases give rise to finite impulse response (FIR) and linear phase FIR subband filtering schemes, respectively. An elegant and simple method of construction of orthonormal wavelet bases employs cardinal B-spline functions. The resulting class of wavelets are known as the Battle-Lemarie wavelets, after G. Battle and P. G. Lemarie who constructed these wavelets independently using different techniques. The chapter aims to study the structural similarity between the fast wavelet algorithm of Mallat and a well-known filtering scheme from digital signal processing. This comparison will prompt us to look at an important class of wavelets.
