Multidimensional 2-channel PR filter banks

General concept of multidimensional (M-D) two-channel perfect reconstruction (PR) filter banks is presented. The framework starts by constructing a factorizable halfband function in M-D and, subsequently, uses spectral factorization to obtain the subband filters. The number of zeros at the aliasing frequency can be obtained easily by using variable transformation from 1-D to M-D. The possible passband shape is discussed. A novel condition for 2-channel PR filter banks in M-D is presented by which the choices of possible passband shapes are significantly reduced. Finally, a frequency mapping between two possible passbands is proposed. A necessary and sufficient condition for the mapping to preserve the PR condition is presented.