A method for the design of a class of 2-D IIR variable cutoff boundary filters

A method of designing a class of 2-D IIR (infinite-impulse-response) filters with a variable cutoff boundary is presented. The transfer function of this class of 2-D filters has a zero-phase two-variable polynomial in z₁ and z ₂ in the numerator and two separable polynomials [D ₁(z₁), D₂(z ₂)] in the denominator. The transformations used for changing the cutoff boundary are A.V. Oppenheim´s (1976) for the numerator and spectral transformations for the denominator of the transfer function. It is demonstrated that the proposed method results in 2-D filters having better circular contours than the existing techniques. This technique also allows one to perform circular-to-elliptic transformation