function x = Adj_Evaluate_FT(y,shift,boxlen,center,w)
% Adj_Evaluate_FT -- 1d unequispaced adjoint Fourier transform
% Usage:
%   x = Evaluate_FT(y,shift,boxlen,center,w)
% Inputs:
%   y	      vector of length 2n
%   shift     vector of shifts
%   boxlen    half length of interval around each value of shift
%   center    boolean variable: 0/1 = unbiased/biased FT
%   w         tapering window of size 2*boxlen
% Outputs:
%   x      vector of length: n
% Description:
%  Evaluates the Adj FT of a signal irregularly sampled in frequency
%                   omega(j,k) = shift(j) + k,  -boxlen <= k <boxlen
%  If center = 0, 
%
%  x(t) = sum_m exp(i 2pi omega(m) t/n) y(k), -n/2 <= t < n/2
%
%  If center = 1, 
%
%  x(t) = sum_m exp(i 2pi omega(m) t/n) y(k), 0 <= t < n
%
%  Adj_Evaluate_FT uses two different methods for computing the
%  unesquispaced Fourier transform. If the number of shifts is less
%  than 8, it uses an exact method, otherwise it uses the
%  accelerated Adjoint USFFT. 
%  See Also
%    Evaluate_FT, Adj_USFFT, Adj_USFT_simple

if nargin < 5,
  w = ones(1,2*boxlen);
end

if nargin < 4,
  center = 0;
end

        n  = length(y)/2;
	boxcnt = length(shift);
	
        if (boxcnt <= 16)
	  x = Adj_USFT_simple(y,shift,boxlen,center,w);
	else
	  % Make grid
	  k = (-boxlen):(boxlen -1);
	  omega = meshgrid(shift,k) + meshgrid(k,shift).';
	  omega = 2*pi*(omega(:))./n;
	  % Multiply by w and take adjoint USFFT
	  y = repmat(w(:),boxcnt,1) .* y;
	  x = Adj_USFFT(n,y,omega,16,6,center)./sqrt(n);
	end