A new design method for IIR diamond-shaped filters

This paper proposes a new design method for two-dimensional diamond-shaped IIR filters. The design starts from a desired 1D prototype filter, to which a frequency transformation is applied, which leads to the 2D filter with the desired shape. The frequency transformation is derived by specifying the filter shape in polar coordinates in the frequency plane. The design method combines the analytical approach with numerical approximations. Starting from a digital prototype filter, we approach two design cases, namely diamond-shaped filters with complex transfer functions, then zero-phase diamond-shaped filters which are particularly useful in image processing due to the absence of phase distortions.