Two-dimensional filters with wideband circularly symmetric frequency response

Two-dimensional filters with circularly symmetric frequency response find application in isotropic filtering of images. An effective method for designing this class of filters is based on applying the McClellan transformation to a one-dimensional prototype. The requirement of wideband circular symmetry necessitates the use of high-order generalized McClellan transformations, where the transformation has to be redesigned as the passband radius increases. In this paper a simple procedure for designing wideband two-dimensional FIR filters with circular symmetry is presented. The procedure is based on combining the low-order original McClellan frequency transformation with a decimation of the resulting 2-D filter impulse response. Conditions to be met by the one-dimensional prototype filter are derived along with the minimum decimation factor required in the design. For given specifications with circular symmetry, it is shown that a solution can always be derived using the fixed low-order transformation