A new class of 2-D digital filters composed of allpass subfilters

The authors present a new synthesis method for 2-D recursive digital filters composed of allpass sub-filters. Some 2-D filters are used for image processing, and in most cases, phase linearity is important as well as amplitude characteristics. Therefore, they consider a parallel connection of an allpass filter and cascaded delays as a basic section to ensure approximately linear phase. First, they review a design method of 1-D digital filters using allpass subfilters and show its property. Furthermore, a new structure for 2-D digital filters with circularly symmetric characteristic is proposed. The proposed filter can be designed directly in the 2-D z-domain by applying 1-D theory. As an example, they design a circularly symmetric lowpass filter to show the effectiveness of the proposed techniques