Linear phase variable 2-D filter design using real-complex decomposition

This paper proposes a new method for designing two-dimensional (2-D) variable digital filters with arbitrary variable magnitude characteristics and linear phases. By combining the given variable magnitude specification with linear phase specification, we first form a variable 2-D frequency response specification. Then we propose a real-complex decomposition method for decomposing the complex-valued variable specification into real-valued and complex-valued components. Finally, the resulting real-valued components are approximated by using 1-D polynomials, and the complex-valued components are approximated by the normal constant 2-D filters. Connecting the 1-D polynomials and 2-D constant filters obtains a variable 2-D filter. The significant advantage of the design method lies in that it can reduce the original difficult problem to a set of easier ones through the real-complex decomposition of the given variable specification.