Existence of optimal paraunitary finite impulse response filter banks for continuous objective functionals

Abstract

The aim of this work is to study the existence and design of perfect reconstruction finite impulse response filter banks that are optimal under explicitly stated criteria. Most of the theoretical results on optimal paraunitary filter banks are developed without restriction on the filter orders. A theorem on the existence of optimal finite impulse response filter banks with respect to continuous objectives is given. This theorem guarantees the existence of optimal filter banks regardless of the bit rate and bit allocation strategy. An algorithm to find these optimal filter banks is given. This algorithm may be used in the design of optimal two-channel finite impulse response filter banks that may be embedded into JPEG-2000 standard for more efficient compression of multicomponent images.