Two-dimensional FIR notch filter design using singular value decomposition

This paper is concerned with the two-dimensional (2-D) linear-phase FIR notch filter-design problem. First, the singular value decomposition (SVD) is used to reduce the 2-D notch filter-design problem to two pairs of one-dimensional (1-D) filter design problems. Then, we derive an analytic least-squares solution for the design of two pairs of 1-D linear-phase FIR filters. Again, the coefficients of the filter designed are given by closed-form formulas and the filter gain at the notch frequencies is exactly zero. One example is included to illustrate the proposed design methods. To demonstrate the usefulness of the 2-D notch filters designed, the 2-D notch filter is applied to eliminate the sinusoidal interference superimposed on an image