1998 Chapters (Layout Features)

Hexagonal QMF Banks and Wavelets

Schuler, Sergio; Laine, Andrew F.

In this chapter we shall lay bare the theory and implementation details of hexagonal sampling systems and hexagonal quadrature mirror filters (HQMF). Hexagonal sampling systems are of particular interest because they exhibit the tightest packing of all regular two-dimensional sampling systems and for a circularly band-limited waveform, hexagonal sampling requires 13.4 percent fewer samples than rectangular sampling. In addition, hexagonal sampling systems also lead to nonseparable quadrature mirror filters in which all basis functions are localized in space, spatial frequency and orientation. This chapter is organized in two sections. Section I describes the theoretical aspects of hexagonal sampling systems while Section II covers important implementation details.