Two-dimensional Linear Phase Orthogonal Filter-banks and Wavelets

Two-dimensional compactly supported, orthogonal wavelets and lter-banks having linear phase are presented. Two cases are discussed, wavelets with twofold symmetry (centrosymmetric), and wavelets with four-fold symmetry that are symmetric (or anti-symmetric) about the vertical and horizontal axes. We show that imposing the requirement of linear phase in the case of factorable wavelets, imposes a simple constraint on each of its polynomial degree-1 factors. We thus obtain a simple and complete method of constructing orthogonal factorable wavelets with linear phase. This method is exempliied by design in the case of four-band separable sampling. An interesting result is obtained, similar to the one well known in 1D case, orthogonal factorable wavelets can not be both continuous and have four-fold symmetry.