A recursive frequency-sampling method for designing zero-phase FIR filters by nonuniform samples

A novel frequency-sampling method for designing zero-phase FIR filters from nonuniform samples is presented. The method is fast, simple, recursive and can be used in the design of 1D or 2D zero-phase FIR filters by imposing some mild constraints on sample locations in the 2D frequency plane. Based on a novel Newton representation of the filter transfer function the proposed method guarantees real results, saves a number of operations and produces accurate solutions even in cases of designing high-order filters or when the interpolation matrix is ill-conditioned. In the progressive case when the next sample appears, the design parameters are evaluated by updating the old ones with correction terms that could be used as indicators for convergence, approximation, or filter reduction. The method can be used in mD filter design, in LU-factorization or in inversion of cosine matrices