Fast algorithm for least squares 2D linear-phase FIR filter design

We develop a new method for weighted least squares 2D linear-phase FIR filter design. It poses the problem of filter design as the problem of projecting the desired frequency response onto the subspace spanned by an appropriate orthonormal basis. We show how to compute the orthonormal basis efficiently in the cases of quadrantally symmetric filter design and centro-symmetric filter design. The design examples show that the proposed method is faster than a conventional weighted least squares filter design method. Also, the amount of storage required to compute the filter coefficients is greatly reduced.