Efficient Analytical Design of Wedge-Shaped Filters

This work presents an analytic design procedure for 2D filters with wedge-shaped frequency response. The design starts from a wide-band, maximally-flat zero-phase low-pass prototype filter, to which a frequency mapping is applied, which leads to the 2D filter with the desired shape. The overall frequency response of the wedge filter is determined in a factored form, and the filter matrices result directly decomposed as a convolution of smaller matrices, a major advantage in implementation. The resulted filter is parametric, being adjustable depending on specifications, namely orientation and aperture angles. Several wedge filter design examples are provided, for various specifications.