function Dj = wavmodwtdet(Wv,J,filtertype);
%% Description
% Computes the Jth detail given a wavelet and scaling vector.
%
% USAGE: Dj is the jth level detail coefficient reconstructed from the
% wavelet coefficients.  To get the coefficients, use taylorMODWT. The
% argument filtertype is the scaling filter to be used in the
% reconstruction process, same as what was used in taylorMODWT.
%
% Example:
% Dj = invmodwt(W,5,'C6_scaling.txt'); 
%
% Returns the jth level detail reconstructed from the wavelet coeffient
% vector Wj. For a reference, consult Percivals text, Wavelet Methods for
% time series analysis.
%
% INPUT: Wv is a vector from the wavelet output matrix from taylorMODWT. J
% is the detail index to be returned, and filtertype is the .txt file
% containing the scaling filter coefficients (like the C6 or Haar).
% OUTPUT: The jth level detail coefficient.  To get all of the detail
% coefficients, loop over wavelet matrix rows, and use W(j,:) at each step
% to compute the jth detail coefficient.  To compute the smooth, subtract
% off the sum of all details from the time series, X.

N = max(size(Wv));


% if(floor(log2(N)) ~= log2(N))
%     disp('Make the time series a power of 2 in length');
% end

% the circular shift matrix
T = spdiags(ones(N,1),-1,N,N);
T(1,end) = 1;

% the wavelet scaling filter
g=load(filtertype);
g=g./(sqrt(2));
L=length(g);

% calculate the wavelet filter 
for l=0:L-1
    h(l+1)=(-1)^(l)*g(L-1-l+1);
end

V=zeros(J,N); %V(J,:)=Sc;
W=zeros(J,N); W(J,:)=Wv;

% calculate inverse MODWT for j=2:J
for j=J:-1:2
    for t=0:(N-1)
        k=t;
	    V(j-1,t+1)=h(0+1)*W(j,k+1)+g(0+1)*V(j,k+1);
        for n=1:(L-1)
            k=k+2^(j-1);
            if k>=N; k=mod(k,N); end
            V(j-1,t+1)=V(j-1,t+1)+h(n+1)*W(j,k+1)+g(n+1)*V(j,k+1);
        end
    end
end


% calculate inverse MODWT for j=1
j=1;
for t=0:(N-1)
    k=t;
    V0(t+1)=h(0+1)*W(j,k+1)+g(0+1)*V(j,k+1);
    for n=1:(L-1)
        k=k+2^(j-1);
        if k>=N; k=mod(k,N); end
        V0(t+1)=V0(t+1)+h(n+1)*W(j,k+1)+g(n+1)*V(j,k+1);
    end
end

Dj=V0;