New interpolatory approximation method with application to the design of multi-dimensional FIR filters

Extended interpolatory approximation method is presented for the n-dimensional (n-D) waves whose spectrums have the weighted L^pnorms smaller than a given positive number. The sample points are selected from a certain subset of the whole vertices of n-D parallelepipeds arranged periodically in Rⁿ. It is assumed that the sample values contain small statistical error. The proposed method minimizes the measure of error which corresponds to the envelope of the standard deviations of the approximation errors. Some important conditions for the convergence of the proposed approximation are presented. Application to the design of n-D FIR filters is also given.