Average-Interpolating Refinement Scheme
fine = AIRefine(coarse,D,Filter,EF)
1-d signal at a coarse scale: length(coarse)=n
D degree of polynomials used for interpolation
interpolating filter from MakeAIFilter(D)
Boundary filter from MakeAIBdryFilter(D)
1-d signal at a fine scale: length(fine) = 2*n
Average-Interpolating Refinement scheme is used to refine boxcar averages on a grid of n points, imputing averages on a finer grid of 2n points.
The average of imputed pairs at (2*i-1,2i) at fine scale reproduce values i at the coarse scale; the pairs are obtained by polynomial interpolation of the coarse averages near i.