Code covered by the BSD License
 analysis(f, J, alpha, tau)% signal is first prefiltered, and then a Jlevel wavelet decomposition
 analysis(inImg, J, alpha,...% First, project the image into the four (tensor) approximation space.
 autocorr(M, alpha)% computes the autocorrelation filter A(z) for the fractional Bspline.
 autocorr(M, alpha)% computes the autocorrelation filter A(z) for the fractional Bspline.
 displayFigures (inImg, w,...% Plots the original and the reconstructed images, and the modulus of the
 displayResults(f, recon, w)% display the original and the reconstructed signal, the real and the
 exception( f )% Checks for inconsistencies.
 exception(f, J)% check and correct for inconsistency.
 filters(M, alpha, tau, flag)% sets up the multiresolution spline filters.
 filters(M, alpha, tau, tag)% Computes the analysis and synthesis filters corresponding to the
 generate.m
 generateGaborWavelets.m
 postfilter(Y, L, alpha, t...% Inverts the prefiltering operation.
 prefilter(im0, alpha, tau...% projects the image onto the four different approximation spaces used in
 projectionFilters(M, alph...% projects the signal onto the four 'matched' approximtion spaces.
 projectionFilters(M, alph...% projects the signal onto the two 'matched' approximtion spaces.
 synthesis(lowpass, w, J, ...% reconstructs the signal from the lowpass signal and the complex wavelet
 synthesis(lowpass, w, J, ...% reconstructs the image from the lowpass signals, and the complex wavelet
 demo.m
 demo.m

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Multiresolution Gaborlike transforms
by
Kunal Chaudhury
11 May 2012
(Updated
14 May 2012)
Matlab implementation of the multiresolution Gabor filters in 1 and 2 dimensions.

autocorr(M, alpha) 
function [A, A2] = autocorr(M, alpha)
%
% computes the autocorrelation filter A(z) for the fractional Bspline.
% A2(z) = A(z^2).
%
nu = (0: 1: M1)/M;
% Nterm approximation
N = 150;
A = zeros(1, M);
for n = N : 1 : N
A = A + abs(sinc(nu + n)).^(2*alpha+2);
end
A2 = [A A];
A2 = A2(1 : 2 : length(A2));


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