A design method of multidimensional linear-phase paraunitary filter banks with a lattice structure

Abstract

A lattice structure of multidimensional (MD) linear-phase paraunitary filter banks (LPPUFBs) is proposed, which makes it possible to design such systems in a systematic manner. Our proposed structure can produce MD-LPPUFBs whose filters all have the region of support /spl Nscr/(M/spl Xi/), where M and /spl Xi/ are the decimation and positive integer diagonal matrices, respectively, and /spl Nscr/(N) denotes the set of integer vectors in the fundamental parallelepiped of a matrix N. It is shown that if /spl Nscr/(M) is reflection invariant with respect to some center, then the reflection invariance of /spl Nscr/(M/spl Xi/) is guaranteed. This fact is important in constructing MD linear-phase filter banks because the reflection invariance is necessary for any linear-phase filter. Since our proposed system structurally restricts both the paraunitary and linear-phase properties, an unconstrained optimization process can be used to design MD-LPPUFBs. Our proposed structure is developed for both an even and an odd number of channels and includes the conventional 1-D system as a special case. It is also shown to be minimal, and the no-DC-leakage condition is presented. Some design examples show the significance of our proposed structure for both the rectangular and nonrectangular decimation cases.