The extended optimum interpolatory approximation of multi-dimensional signals

The optimum space-limited interpolation functions are presented which minimize simultaneously the wide variety of measures of error defined independently in each separate block in the space variable domain. For this approximation, certain reciprocal relation holds. Although the quantization of the decimated sample values is contained in this discussion, the proposed approximation has the favorable property stated above. An interesting equivalent transformation for filter banks having a tree structure is considered. As applications, we present several examples of cosine modulated filter bank and linear phase filter banks designed by simple iterative linear approximation based on the reciprocal relation