Design of two-dimensional Allpass filters using Hilbert transform

A new design method for two-dimensional allpass filters to approximate the desired phase characteristic is proposed in this paper. Considering the denominator polynomial of the allpass transfer function, the design method via Hilbert transform is expanded to a two dimensional case complex coefficients. When the Hilbert transform is used, a problem arises in that sometimes truncating coefficients cause the filter to be unstable. In this paper, in an unstable case, the resultant frequency response is approximated as a low-order polynomial by using the Lagrange interpolation technique and the same procedures are repeated. Therefore, this proposed method ensures the stability of the designed filter because the coefficients of order higher than the desired order are small enough to be almost zero.