Design of linear phase variable 2-D digital filters using real-complex decomposition

Variable digital filters are especially difficult to design when the given variable design specifications are complicated. This paper proposes a new method for designing two dimensional (2-D) variable digital filters with arbitrarily variable, magnitude characteristics and linear phase. By combining variable magnitude specification with linear phase specification, we first form a variable 2-D frequency response specification, which is complex-valued. Then we propose a method for decomposing the complex-valued variable specification into real-valued and complex-valued components. We call this decomposition the Real Complex decomposition. Finally, the resulting real-valued components are approximated by using one-dimensional (1-D) polynomials, and the complex-valued components are approximated by using constant 2-D filters. Connecting the 1-D polynomials and 2-D constant filters results in a variable 2-D filter. The significant advantage of the design method is that it can reduce the original difficult problem to a set of easier ones based on the Real-Complex decomposition.