Design Approach for 2D Recursive Filters Used in Frequency Plane Partitioning

This work proposes an analytical design procedure for some types of 2D recursive filters useful in frequency plane partitioning, namely diamond, parallelogram, fan or wedge-shaped filters with a specified bandwidth and orientation. Such filters can be used as components of particular filter banks, applied in directional image decomposition. The design starts from two zero-phase low-pass 1D prototypes, to which specific frequency mappings are applied, also exploiting the symmetry properties in the frequency plane. This method combines analytical approach with numerical approximations, yielding the desired 2D frequency response. A more selective filter results by combining two or several elementary filters. Several design examples for these filters are provided.