# csdms-contrib/slepian_echo

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 function varargout=d2boxstep(x,level,dim,cofs) % f=D2BOXSTEP(x,level,dim,cofs) % % Performs one FORWARD iteration (ending at a certain level of % decomposition) of D2 transform along a certain dimension; putting % scaling coefficients in front, followed by wavelet coefficients. This % transform is an isometry. It is equal to the Haar transform. % % INPUT: % % x The three-dimensional array, sized as a power of two % level The level we end up at [scalar] % dim The index identifying the dimension [scalar] % cofs The wavelet and scaling filter coefficients [D2BOXCOF] % % OUTPUT: % % f The wavelet transform of x, same dimensions as x % % EXAMPLE: My forward is the inverse of my inverse % d2boxstep('demo1') % % SEE ALSO: D2BOXSTEPI, D2BOXCOF % % Inspired by Ignace Loris (igloris@vub.ac.be) on 22.06.2009 % Last modified by fjsimons-at-alum.mit.edu, 08/24/2010 if ~isstr(x) % Initialize output, which you need to always take from the previous step f=x; if level==0 % Do nothing varargout={f}; return end % Figure out dimensions nall=size(x); if length(nall)==2 nall(3)=1; end % To move into 'level' we split 2^(n-level+1) coefficients into two sets % of k coefficients each, where 2^n is the dimension of the data set k=size(x,dim)/2^level; % The LF-tap filter length LF=length(cofs.H0); if k<=2^(LF/2); warning('Input signal is not long enough for reconstruction'); end % Exclude the same number on the left and right, namely none for i=1:k % Isolate the DOWNSAMPLED sets of planes in the right dimension xinside=[x(dindeks(2*i+0,dim,nall))'; ... x(dindeks(2*i-1,dim,nall))']; % And put the convolutions in the right spot % See under ANALYSIS, SN p. 123 % Interior, Lowpass (Scaling Coefficients) f(dindeks( i,dim,nall))=cofs.H0*xinside; % Interior, Highpass (Wavelet Coefficients) f(dindeks(k+i,dim,nall))=cofs.H1*xinside; end % All other coefficients (wavelet coeff from previous step) remain varargout={f}; elseif strcmp(x,'demo1') cofs=d2boxcof; dim=ceil(rand*3); % Random-sized array must be at least 2^3 long n=ceil(rand*7+3); % Edge treatment only accurate to level 0 if it is 2^3 long level=ceil(rand*(n-3)); % The random data if dim==1 x=rand([2^n 1 1 ]); elseif dim==2 x=rand([1 2^n 1 ]); elseif dim==3 x=rand([1 1 2^n]); end % Initial output disp(sprintf('\n====== D2BOXSTEP versus D2BOXSTEPI ===== \n')) disp(sprintf('n = %i ; lev = %i ; dim = %i',n,level,dim)) % The forward transform xf=d2boxstep(x,level,dim,cofs); % The inverse of the forward transform xfi=d2boxstepi(xf,level,dim,cofs); % The reconstruction error, should be zero mae1=mean(mean(mean(abs(x-xfi)))); % Further output % Further output disp(sprintf('no preconditioning mean(abs(error)) = %8.3e',mae1)) disp(sprintf('\n======================================= \n')) end