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 realizing sharp one-dimensional (1-D) filters. Sharp 1-D filters realized using the FRM technique have considerably lower complexity than those realized in the direct form. In this paper, we present an extension of the FRM technique 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 transition width of the desired DS filter is very narrow. An expression for the impulse response up-sampling ratio that produces the design with the least complexity is derived. Extensions of the technique for the synthesis of 2-D filters other than the DS filters are also discussed.