Comparison of orthogonal and biorthogonal wavelets for multicarrier systems

Abstract

Wavelets are constructed from the basis sets of their parent scaling functions of the two-scale dilation equation (1). Whereas orthogonal wavelets come from one orthogonal basis set, the biorthogonal wavelets project from different basis sets. Each basis set is correspondingly weighted to form filters, either highpass or lowpass, which form the constituents of quadrature mirror filter (QMF) banks. Consequently, these filters can be used to design wavelets, the differently weighted parameters contributing respective wavelet properties which influence the performance of the transforms in applications, for example multicarrier modulation. This study investigated applications for onward multicarrier modulation applications. The results show that the optimum choice of particular wavelet adopted in digital multicarrier communication signal processing may be quite different from choices in other areas of wavelet applications, for example image and video compression.