Polynomial methods for multi-dimensional filter banks' design

The problem of the design of multi-dimensional filter banks with prescribed properties is considered. The most important requirements are perfect reconstruction property, linear phase property, optimization for a given class of signals, maximum number of vanishing moments and others. A survey of different approaches to this problem proves that the most promising are polynomial approaches that allow to find the result directly in analytical form. The results of filter banks' optimization are presented (so that the stop-band energy of the filter is minimum in the least-squares sense).