On paraunitary filter banks and wavelets with the linear-phase and mirror-image properties

Several lattice structures for designing and implementing paraunitary filter banks have been proposed in the past. It has also been shown that the number of parameters required to characterize the structures can be significantly reduced if the linear-phase (LP) or the pairwise mirror-image frequency response (PWMIFR) constraints are structurally imposed. In this paper, a lattice structure for paraunitary filter banks with filters that satisfy both the LP and PWMIFR properties is developed. It is shown that this structure is complete and uses fewer parameters than previously proposed structures. The new structure is generalized to the case of filter banks with variable length filters and is also used to construct wavelets with up to two degrees of regularity. A central role in this development is played by the theory of symmetric orthogonal matrices. Within the framework of this paper, these matrices are used to characterize the new lattice and to construct wavelets with the desired degree of regularity.