Some design methods for two-dimensional digital filters with complex coefficients in consideration of linear phase characteristics

A comparatively simple design technique for a 2-D digital filter with complex coefficients is presented taking phase into consideration. The 1-D real coefficient FIR filter is shifted and a transformation of variables is used to obtain the 2-D filter. In this method, the sharpness of cutoff and circular symmetry can be controlled by independent parameters. A design example using the method is presented. A design technique for a recursive digital filter with constant group delay characteristics using a 2-D mirror image polynomial with complex coefficient is considered, including a design example. The general properties of the 2-D analytic signal are also discussed.