Symmetry conditions for 2-D complex irreducible polynomials

Constraints on analog and digital complex irreducible polynomials are given, such that they possess different types of symmetries, such as centrosymmetry, quadrantal symmetry, diagonal symmetry, four-fold rotational symmetry, and octagonal symmetry, in their magnitude responses. The symmetries present in the phase responses of these polynomials are also discussed. It is further shown that the 3-D single planar symmetry results for real polynomials have special relations to the 2-D symmetry results for complex polynomials, and that the 2-D symmetry results for 2-D real polynomials are special cases of those for the complex polynomials.<>