Design of zero-phase, multiform, tiltable two-dimensional filters

This paper advances a novel and relatively simple scheme for designing two-dimensional (2-D) filters with zero phase. The proposed filters are obtained by a nonlinear mapping of a one-dimensional (1-D) magnitude response into a 2-D filter. By appropriately constraining the filter parameters, a wide variety of passband iso-contour shapes can be generated in the frequency-frequency plane, e.g., tilted or untilted ellipses, circles, diamonds, parallel strips at arbitrary angles, crosses, and “snowflakes”. Simple equations for designing the filter´s parameters that meet or exceed user specifications are given for the special cases when the 1-D prototype is the magnitude response of a Gaussian, Butterworth, Chebyshev, or inverse Chebyshev filter. A scheme for designing fan filters with arbitrary angle is also provided