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).