Some results on the nature of a 2-dimensional filter function possessing certain symmetry in its magnitude response

Constraints on analogue and digital two-dimensional filter functions so that they possess various symmetries like quadrantal symmetry and circular symmetry in their magnitude responses are derived. An ideal circularly symmetric separable magnitude squared function is obtained. Approximation of the ideal function in analogue and digital domain is carried out and the contour plots of the responses of the resulting functions show that they are very nearly circularly symmetric.