Two-Channel, Separable, Complex, Orthogonal, Perfect Reconstruction Filter Banks and Wavelets

This paper demonstrates the design of separable complex orthogonal perfect reconstruction filters (OPRFs), which are defined to be complex OPRPs in which the real or imaginary part is also a valid OPRF. Separable filters greatly simplify the task of designing complex OPRFs by reducing it to a two step process: design a real OPRF (using now well known methods), then finding a "complex complementary" filter that results in an overall complex OPRF This paper parameterizes, given any real OPRF, filters complex complementary to it. The parameterization is based on simple angle relationships in the lattice representation of each filter. Also shown is a simple method for designing complex wavelets from separable complex OPRFs.