danieleb@0: function g = lappedwindow(wLength,tailLength,tailFunc,special)
danieleb@15: %LAPPEDWINDOW lapped window for lapped orthogonal transform
danieleb@0: %
danieleb@14: % Example
danieleb@0: % g = lappedwindow(wLength,tailLength,tailFunc,special)
danieleb@0: %
danieleb@14: % Input:
danieleb@0: % - wLength: length of the window
danieleb@4: % - tailLength: (optional, default=floor(wLength/2))length of the tail of 
danieleb@4: % the overlapping window. 
danieleb@0: %
danieleb@0: %     ......................
danieleb@0: %   |.                      .|
danieleb@0: %   .                        .
danieleb@0: %  .|                        |.
danieleb@0: % . |---------wLength--------| .
danieleb@0: %                            |-| 
danieleb@0: %                         tailLength
danieleb@0: %
danieleb@0: % The maximum tailLength cannot exceed half the window length. 
danieleb@4: % - tailFunc: (optional, default='sin2') either a string or a function 
danieleb@4: % handle used to define the tails of the overlapping windows. The default 
danieleb@4: % is 'sin2' (twicely differentiable sinusoidal).
danieleb@0: %
danieleb@14: % Output:
danieleb@0: % - g: vector containing the window
danieleb@0: %
danieleb@14: % Reference:
danieleb@0: % S. Mallat, A Wavelet Tour of Signal Processing
danieleb@0: %
danieleb@14: % See also lot, ilot
danieleb@4: 
danieleb@4: % Author(s): Daniele Barchiesi
danieleb@14: % Copyright 2011-2011
danieleb@0: 
danieleb@0: %% Check inputs
danieleb@4: error(nargchk(1, 4, nargin, 'struct'));
danieleb@0: if ~exist('special','var') || isempty(special), special = []; end
danieleb@4: if ~exist('tailFunc','var') || isempty(tailFunc), tailFunc = 'sin2'; end
danieleb@4: if ~exist('tailLength','var') || isempty(tailLength), tailLength = floor(wLength/2); end
danieleb@0: 
danieleb@0: %check that the window is not too short
danieleb@0: if wLength<2*tailLength
danieleb@0:     error('the window length must be at least twice as long as the tail length');
danieleb@0: end
danieleb@0: 
danieleb@0: %manage tail function
danieleb@0: if ischar(tailFunc)
danieleb@0:     [fname iter] = parsefunctionname(tailFunc);
danieleb@0:     switch lower(fname)
danieleb@0:         case 'sin'
danieleb@0:             tailFunc = @(x)sin((pi/4)*(x+1));
danieleb@0:         otherwise
danieleb@0:             error('invalid tail function');
danieleb@0:     end
danieleb@0:     if iter
danieleb@0:         for i=1:iter
danieleb@0:             tailFun = @(x)tailFun(sin(pi*x/2));
danieleb@0:         end
danieleb@0:     end
danieleb@0: else %if a function handler, check that it corresponds to a valid tail.
danieleb@0:     t = linspace(-1,1,1000);
danieleb@0:     test = norm((tailFunc(t).^2)+(tailFunc(fliplr(t)).^2)-ones(1,length(t)));
danieleb@0:     if test>1e-8
danieleb@0:         error('invalid tail function');
danieleb@0:     end
danieleb@0: end
danieleb@0: 
danieleb@0: %% construct the window
danieleb@0: if ~isempty(special)
danieleb@0:     g = ones(wLength+tailLength,1);
danieleb@0:     g(1:2*tailLength) = tailFunc((-tailLength+0.5:tailLength-0.5)'/tailLength);
danieleb@0:     if strcmpi(special,'first')
danieleb@0:         g = flipud(g);
danieleb@0:     end
danieleb@0: else
danieleb@0:     g = ones(wLength+2*tailLength,1);
danieleb@0:     g(1:2*tailLength) = tailFunc((-tailLength+0.5:tailLength-0.5)'/tailLength);
danieleb@0:     g(wLength+1:wLength+2*tailLength) = ...
danieleb@0:         flipud(tailFunc((-tailLength+0.5:tailLength-0.5)'/tailLength));
danieleb@0: end
danieleb@0: 
danieleb@0: function [fname iter] = parsefunctionname(tailFunc)
danieleb@0: nameLen = length(tailFunc);
danieleb@0: for i=1:nameLen
danieleb@0:     if real(str2double(tailFunc(i)))>0
danieleb@0:         fname = tailFunc(1:i-1);
danieleb@0:         iter = uint16(str2double(tailFunc(i:end)));
danieleb@0:         return
danieleb@0:     end
danieleb@0: end
danieleb@0: fname = tailFunc;
danieleb@0: iter = [];