runline

 Running line fit (local linear regression)

 Usage: y_line=runline(y,n,dn);

 Inputs: 
 y: input 1-d time series (real)
 n: length of running window in samples
 dn: stepsize of window in samples
 
 Outputs:
 y_line: local line fit to data

0001 function y_line=runline(y,n,dn)
0002 % Running line fit (local linear regression)
0003 %
0004 % Usage: y_line=runline(y,n,dn);
0005 %
0006 % Inputs:
0007 % y: input 1-d time series (real)
0008 % n: length of running window in samples
0009 % dn: stepsize of window in samples
0010 %
0011 % Outputs:
0012 % y_line: local line fit to data
0013 y=y(:);
0014 nt=length(y);
0015 y_line=zeros(nt,1);
0016 norm=y_line;
0017 nwin=ceil((nt-n)/dn);
0018 yfit=zeros(nwin,n);
0019 xwt=((1:n)-n/2)/(n/2);
0020 wt=(1-abs(xwt).^3).^3;
0021 for j=1:nwin, 
0022     tseg=y(dn*(j-1)+1:dn*(j-1)+n);
0023     y1=mean(tseg); 
0024     y2=mean((1:n)'.*tseg)*2/(n+1);
0025     a=(y2-y1)*6/(n-1); b=y1-a*(n+1)/2;
0026     yfit(j,:)=(1:n)*a+b;
0027     y_line((j-1)*dn+(1:n))=y_line((j-1)*dn+(1:n))+(yfit(j,:).*wt)';
0028     norm((j-1)*dn+(1:n))=norm((j-1)*dn+(1:n))+wt';
0029 end
0030 mask=find(norm>0); y_line(mask)=y_line(mask)./norm(mask);
0031 indx=(nwin-1)*dn+n-1;
0032 npts=length(y)-indx+1;
0033 y_line(indx:end)=(n+1:n+npts)'*a+b;