?? airefine.m
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function a2 = AIRefine(a,D,Filter,EdgeFilter)
% AIRefine -- Average-Interpolating Refinement Scheme
% Usage
% fine = AIRefine(coarse,D,Filter,EF)
% Inputs
% coarse 1-d signal at a coarse scale: length(coarse)=n
% D D degree of polynomials used for interpolation
% Filter interpolating filter from MakeAIFilter(D)
% EF Boundary filter from MakeAIBdryFilter(D)
% Outputs
% fine 1-d signal at a fine scale: length(fine) = 2*n
%
% Description
% 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.
%
% See Also
% AIDyadUp, AIDyaAIown, FWT_AI, IWT_AI
%
n = length(a); n2 = 2*n; a2 = zeros(1,n2);
ae = [ a; 0 .*a ]; ae = ae(:)';
temp = conv(Filter,ae);
a2((D+1):(n2-D)) = temp((2*D+1):(n2));
%
% Adjustments at edges
%
a2(1:D) = EdgeFilter * (a(1:(D+1))');
a2((n2-D+1):n2) = reverse(EdgeFilter * (reverse(a((n-D):n))'));
%
% Part of WaveLab Version 802
% Built Sunday, October 3, 1999 8:52:27 AM
% This is Copyrighted Material
% For Copying permissions see COPYING.m
% Comments? e-mail wavelab@stat.stanford.edu
%
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