Design of Two-Band Critically Sampled Rational Rate Filter Banks With Multiple Regularity Orders and Associated Discrete Wavelet Transforms

An approach for designing two-band rational rate critically sampled nonorthogonal filter banks with perfect reconstruction and multiple regularity orders is proposed. This approach relies on an updated result on the relationship between the filters in the filter bank to achieve all the desired properties. Filter responses are optimized to approximate ideal brick wall responses, subject to linear and nonlinear constraints derived from regularity and perfect reconstruction conditions, respectively. The obtained designs are approximately shift-invariant as a result of strong frequency selectivity and multiple regularity orders. Two methods for solving the nonconvex optimization design problem are presented and the results from the proposed approach are compared against existing designs in the literature.