samer@4: function m=mapwindows(fn,x,L,M)
samer@4: % mapwindows - Apply function to windowed signal with causality control
samer@4: %
samer@4: % mapwindows ::
samer@4: %    F:([[N]]->[[M]]) ~'function to apply to windowed segments',
samer@4: %    [[T]]            ~'signal of length T',
samer@4: %    L:natural        ~'post-window (ie causal part)',
samer@4: %    M:natural        ~'pre-window (ie anti-causal part)'
samer@4: % -> [[M,T]]          ~'sequence of results'.
samer@4: %
samer@4: % This function applies a function to a sequence of segments extracted from
samer@4: % the given signal by sliding a window along the signal. The
samer@4: % post- and pre- window lengths determine the positioning of the window:
samer@4: %
samer@4: %    ....   x1   x2   x3   x4   x5    x6   x7   x8   x9  ...
samer@4: %         |<--- post --> | now |<----- pre ------> |
samer@4: %         \________________________________________/
samer@4: %                           |
samer@4: %                       function
samer@4: %                           |
samer@4: %               ...   y3   y4   y5 ...
samer@4: %
samer@4: % Note: the function F must make sense when applied to windows of
samer@4: % different lengths since the first and last few windows will
samer@4: % be shorter than L+M+1. The windows will not be zero padded!
samer@4: %
samer@4: % EXAMPLES
samer@4: %
samer@4: % To compute a running mean using only past values (ie causally)
samer@4: % >> Y=mapwindows(@mean,X,6,0);
samer@4: %
samer@4: % To compute a running local median
samer@4: % >> Y=mapwindows(@median,X,4,3);
samer@4: 
samer@4: N=length(x);
samer@4: 
samer@4: for i=1:min(L,N)
samer@4: 	k=min(i+M,N);
samer@4: 	MM=feval(fn,x(1:k));
samer@4: 	m(:,i)=feval(fn,x(1:k));
samer@4: end
samer@4: 
samer@4: if N>(L+M)
samer@4: 	m=[m feval(fn,buffer(x,L+M+1,L+M,'nodelay'))];
samer@4: end
samer@4: 
samer@4: for i=N+(1-M:0)
samer@4: 	j=max(i-L,1);
samer@4: 	m(:,i)=feval(fn,x(j:end));
samer@4: end
samer@4: