Design of stable two-dimensional IIR notch filter using root map

In this paper, the two-dimensional (2-D) IIR notch filter design problem is presented. First, the linear fractional transformation (LFT) in complex analysis is used to construct the desired root map of 2-D polynomial. Then, the numerator and denominator of transfer function of 2-D IIR notch filter can be obtained from the LFT used in the construction of root map. This design not only has closed-form transfer function but also satisfies the bounded input/bounded output (BIBO) stability condition. Finally, design example and image application are demonstrated to show the effectiveness of the proposed approach.