A 2-D block decomposition technique for designing 2-D FIR filters from frequency samples

A new technique for computing the coefficients of a class of 2-D polynomials from samples that are located anywhere in the plane or distributed on curves with desired shapes is presented. The algorithm is based on a 2-D block decomposition technique suitable for deriving the LU products of the interpolation matrix. A variation of this technique leads to an efficient solution of 2-D interpolation problems for which the interpolation points occur in complex conjugate pairs but where the coefficients of the interpolation polynomial are real. These results are applied in designing 2-D FIR filters. The algorithm proposed permits all operations to be performed by real arithmetic, guarantees real results, saves a number of operations, and produces accurate solutions, even in case of designing high-order 2-D FIR filters or when the interpolation matrix is ill conditioned. The algorithm is well suited to parallel computations and can be extended to design m-D FIR digital filters or to invert m-D interpolation matrices