Polynomial approximations of interpolants

The use of filtering paradigms to discuss sample rate changing has received significant attention over the last 25 years. Interpolation, decimation and fractional structures for changing the sample rate based on anything from simple methods such as zero-order hold and linear interpolation to complex filtering structures which approach Shannon's ideal reconstruction formula in some sense (so-called perfect reconstruction techniques) have been proposed, along with supporting design techniques. In this paper we show a powerful technique, sufficiently general to model any choice of interpolating function as a simple jittering process that can easily be extended to any number of dimensions. We apply the technique to image zooming and discuss some results.