Design of recursive quadrant fan filters

A quadrant fan filter is a fan filter whose four pass and stop regions (sectors) coincide with the four quadrants of the two-dimensional frequency plane. A design method for stable recursive quadrant fan filters is presented. This method is based on the classical image parameter method and is such that arbitrary close specifications in the pass and stop regions can be met. The resulting transfer function can be realized by any suitable general structure for implementing two-dimensional digital filters. More specifically, however, a realization by a two-dimensional lattice wave digital filter is always possible. An extension to fan filters with pass or stop sectors narrower than 90 deg is discussed.