2-D two-fold symmetric circular shaped filter design with homomorphic processing application

A design method of a linear-phased, two-dimensional (2-D), two-fold symmetric circular shaped filter is presented in this paper. Although the proposed method designs a non-separable filter, its implementation has linear complexity. The shape of the passband and the stopband is expressed in terms of level sets of second order trigonometric polynomials. This enables the transformation of the filter specifications to a Semi-Definite Program (SDP) of moderate dimension. The proposed filter outperforms currently available filter design methods. We present a performance comparison, as well as a homomorphic processing image enhancement example to illustrate the effectiveness of this method.