function [yl,yh,L] = mrdwt(x,h,L);%    [yl,yh,L] = mrdwt(x,h,L);% %    Function computes the redundant discrete wavelet transform y%    for a 1D  or 2D input signal. (Redundant means here that the%    sub-sampling after each stage is omitted.) yl contains the%    lowpass and yh the highpass components. In the case of a 2D%    signal, the ordering in yh is %    [lh hl hh lh hl ... ] (first letter refers to row, second to%    column filtering). %%    Input:%	     x : finite length 1D or 2D signal (implicitly periodized)%       h : scaling filter%       L : number of levels. In the case of a 1D %           length(x) must be  divisible by 2^L;%           in the case of a 2D signal, the row and the%           column dimension must be divisible by 2^L.%           If no argument is%           specified, a full DWT is returned for maximal possible L.%   %    Output:%       yl : lowpass component%       yh : highpass components%       L  : number of levels%%  HERE'S AN EASY WAY TO RUN THE EXAMPLES:%  Cut-and-paste the example you want to run to a new file %  called ex.m, for example. Delete out the % at the beginning %  of each line in ex.m (Can use search-and-replace in your editor%  to replace it with a space). Type 'ex' in matlab and hit return.%%%    Example 1::%    x = makesig('Leopold',8);%    h = daubcqf(4,'min');%    L = 1;%    [yl,yh,L] = mrdwt(x,h,L)%    yl =  0.8365  0.4830 0 0 0 0 -0.1294 0.2241%    yh = -0.2241 -0.1294 0 0 0 0 -0.4830 0.8365%    L = 1%    Example 2:%    load lena;%    h = daubcqf(4,'min');%    L = 2;%    [ll_lev2,yh,L] = mrdwt(lena,h,L); % lena is a 256x256 matrix%    N = 256;%    lh_lev1 = yh(:,1:N); %    hl_lev1 = yh(:,N+1:2*N); %    hh_lev1 = yh(:,2*N+1:3*N);%    lh_lev2 = yh(:,3*N+1:4*N); %    hl_lev2 = yh(:,4*N+1:5*N); %    hh_lev2 = yh(:,5*N+1:6*N);%    figure; colormap(gray); imagesc(lena); title('Original Image');%    figure; colormap(gray); imagesc(ll_lev2); title('LL Level 2');%    figure; colormap(gray); imagesc(hh_lev2); title('HH Level 2');%    figure; colormap(gray); imagesc(hl_lev2); title('HL Level 2');%    figure; colormap(gray); imagesc(lh_lev2); title('LH Level 2');%    figure; colormap(gray); imagesc(hh_lev1); title('HH Level 1');%    figure; colormap(gray); imagesc(hl_lev2); title('HL Level 1');%    figure; colormap(gray); imagesc(lh_lev2); title('LH Level 1');%           %    See also: mdwt, midwt, mirdwt%%    Warning! min(size(x))/2^L should be greater than length(h)%%File Name: mrdwt.m%Last Modification Date: 08/07/95	15:14:47%Current Version: mrdwt.m	2.4%File Creation Date: Wed Oct 19 10:51:58 1994%Author: Markus Lang  <lang@jazz.rice.edu>%%Copyright (c) 2000 RICE UNIVERSITY. All rights reserved.%Created by Markus Lang, Department of ECE, Rice University. %%This software is distributed and licensed to you on a non-exclusive %basis, free-of-charge. Redistribution and use in source and binary forms, %with or without modification, are permitted provided that the following %conditions are met:%%1. Redistribution of source code must retain the above copyright notice, %   this list of conditions and the following disclaimer.%2. Redistribution in binary form must reproduce the above copyright notice, %   this list of conditions and the following disclaimer in the %   documentation and/or other materials provided with the distribution.%3. All advertising materials mentioning features or use of this software %   must display the following acknowledgment: This product includes %   software developed by Rice University, Houston, Texas and its contributors.%4. Neither the name of the University nor the names of its contributors %   may be used to endorse or promote products derived from this software %   without specific prior written permission.%%THIS SOFTWARE IS PROVIDED BY WILLIAM MARSH RICE UNIVERSITY, HOUSTON, TEXAS, %AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, %BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS %FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL RICE UNIVERSITY %OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, %EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, %PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; %OR BUSINESS INTERRUPTIONS) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, %WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR %OTHERWISE), PRODUCT LIABILITY, OR OTHERWISE ARISING IN ANY WAY OUT OF THE %USE OF THIS SOFTWARE,  EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.%%For information on commercial licenses, contact Rice University's Office of %Technology Transfer at techtran@rice.edu or (713) 348-6173%%Change History:% %Modification #1%Mon Aug  7 14:26:26 CDT 1995%Rebecca Hindman <hindman@ece.rice.edu>%Added L to function line so that it can be displayed as an output% %Thursday Mar 2 2000% Added Example 2% Felix Fernandes <felixf@rice.edu>