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Analytical two-dimensional IIR notch filter design using outer product expansion

This work is concerned with the two-dimensional (2-D) digital notch filter design problem. First, the outer product expansion is used to reduce the 2-D notch filter design problem to two pairs of one-dimensional (1-D) filter design problems. Then, we develop a simple algebraic method for the design of two pairs of 1-D IIR filters. This approach not only has closed form transfer function but also satisfies bounded input/output (BIBO) stability condition. Finally, one example is included to illustrate the proposed design method, and the 2-D IIR notch filter is applied to eliminate the sinusoidal interference superimposed on an image.