Fourfold rotational symmetry in two-dimensional functions

The presence of various types of symmetry in the frequency responses of a two-dimensional filter function reflects as constraints on its coefficients. In this paper, such constraints are derived for two-dimensional analog and digital transfer functions so that the magnitude functions of the frequency responses of these transfer functions possess fourfold rotational symmetry. The relationship between fourfold rotational symmetry and quadrantal, diagonal, and octagonal symmetries is also discussed.