Frequency-response masking approach for the synthesis of sharp two-dimensional diamond-shaped filters

The frequency-response masking (FRM) technique is an efficient method for r ealizing sharp one-dimensional (1-D) filters. Sharp 1-D filters realized us ing the FRM technique have considerably lower complexity than those realize d in the direct form. In this paper, we present an extension of the FRM tec hnique to the synthesis of sharp two-dimensional (2-D) diamond-shaped (DS) filters. The new technique, based upon dividing the frequency spectrum into four complementary components and the utilization of four masking filters, achieves large reductions in filter implementation complexity when the tra nsition width of the desired DS filter is very narrow. An expression for th e impulse response up-sampling ratio that produces the design with the leas t complexity is derived. Extensions of the technique for the synthesis of 2 -D filters other than the DS filters are also discussed.