A study of two-channel complex-valued filterbanks and wavelets with orthogonality and symmetry properties

We investigate two-channel complex-valued filterbanks and wavelets that simultaneously have orthogonality and symmetry properties. First, the conditions for the filterbank to be orthogonal, symmetric, and regular (for generating smooth wavelets) are presented. Then, a complete and minimal lattice structure is developed, which enables a general design approach for filterbanks and wavelets with arbitrary length and arbitrary order of regularity. Finally, two integer implementation methods that preserve the perfect reconstruction property of the filterbank are proposed. Their performances are evaluated via experimental results.