Theory and lattice structure of complex paraunitary filterbanks with filters of (Hermitian-)symmetry/antisymmetry properties

The theory of the real-coefficient linear-phase filterbank (LPFB) is extended to the complex case in two ways, leading to two generalized classes of M-channel filterbanks. One is the symmetric/antisymmetric filterbank (SAFB), where all filters are symmetric or antisymmetric. The other is the complex linear phase filterbank (CLPFB), where all filters are Hermitian symmetric or Hermitian antisymmetric and, hence, have the linear-phase property. Necessary conditions on the filter symmetry polarity and lengths for the existence of permissible solutions are investigated. Complete and minimal lattice structures are developed for the paraunitary SAFE and paraunitary CLPFB, where the channel number M is arbitrary (even or odd), and the subband filters could have different lengths. With the elementary unitary matrices in the structure of the paraunitary SAFE constrained to be real and orthogonal, the structure covers the most general real-coefficient paraunitary LPFBs. Compared with the existing results, the number of parameters is reduced significantly.