Non-Separable Two-Dimensional Perfect Reconstruction Filter Banks

Non-separable filter banks are studied for general two-dimensional sub-band coding. The developed results are valid for any sub-sampling pattern. A synthesis structure is given which enables cascade-structure design of all two-dimensional paraunitary perfect reconstruction filter banks. The resulting structure is evaluated with regard to free variables and computational complexity. The synthesis structure is also extended to embrace non-paraunitary perfect reconstruction systems. Finally, conditions are derived to test filter banks for linear phase in the polyphase domain.