Two-dimensional orthogonal filter banks and wavelets with linearphase

Authors:
D. Stanhill;Y.Y. Zeevi
Affiliations:
Dept. of Electr. Eng., Technion-Israel Inst. of Technol., Haifa;-
Venue:
IEEE Transactions on Signal Processing
Year:
1998

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Abstract

Two-dimensional (2-D) compactly supported, orthogonal wavelets and filter banks having linear phase are presented. Two cases are discussed: wavelets with two-fold 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 order-factorable wavelets imposes a simple constraint on each of its polynomial order-1 factors. We thus obtain a simple and complete method of constructing orthogonal order-factorable wavelets with linear phase. This method is exemplified by design in the 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 obtained: orthogonal order-factorable wavelets cannot be both continuous and have four-fold symmetry