2-DIMENSIONAL ORTHOGONAL FILTER BANKS AND WAVELETS WITH LINEAR-PHASE

Two-dimensional (2-D) compactly supported, orthogonal wavelets and fil ter banks having linear phase are presented, Two cases are discussed: wavelets with two-fold symmetry (centrosymmetric) and wavelets with fo ur-fold symmetry that are symmetric (or anti-symmetric) about the vert ical and horizontal axes. We show that imposing the requirement of lin ear phase in the case of order-factorable wavelets imposes a simple co nstraint on each of its polynomial order-1 factors, We thus obtain a s imple and complete method of constructing orthogonal order-factorable wavelets with linear phase, This method is exemplified by design in th e case of four-band separable sampling. An interesting result that is similar to the one well-known in the one-dimensional (1-D) case is obt ained: Orthogonal order-factorable wavelets cannot be both continuous and have four-fold symmetry.