function y = Evaluate_FT(x,shift,boxlen,center,w)
% Evaluate_FT -- 1d unequispaced Fourier transform followed by windowing
% Usage:
%   y = Evaluate_FT(x,shift,boxlen,center,w)
% Inputs:
%   x	      vector of length n
%   shift     vector of shifts
%   boxlen    half length of interval around each shift
%   center    boolean variable: 0/1 = unbiased/biased FT
%   w         tapering window of size 2*boxlen
% Outputs:
%   y         vector of length: (# shifts) * (2*boxlen)
% Description:
%  Evaluates the FT at the frequency points 
%                   omega(j,k) = shift(j) + k, -boxlen <= k <boxlen
%  If center = 0, 
%
%  y = sum_{-n/2 <= t < n/2} exp(-i 2pi omega t/n) x(t), -n/2 <= t < n/2
%
%  If center = 1, 
%
%  y = sum_{0 <= t < n} exp(-i 2pi omega t/n) x(t), 0 <= t < n
%
%  For each shift parameter (shift(j)), the outcome y_j is then
%  tapered with the window w
%
%  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 USFFT. 
%  See Also
%    Adj_Evaluate_FT, USFFT, USFT_simple
% 
% By Emmanuel candes, 2003-2004

  if nargin < 5,
    w = ones(1,2*boxlen);
  end
  
  if nargin < 4,
    center = 0;
  end
  
  n = length(x);
  boxcnt = length(shift);
  
  if (boxcnt <= 16)
	  y = USFT_simple(x,shift,boxlen,center,w); % nonequispaced FT
  else
    % Make frequency grid
    k = (-boxlen):(boxlen -1);
    omega = meshgrid(shift,k) + meshgrid(k,shift).';
    omega = 2*pi*(omega(:))./n;
   
    y = USFFT(x,omega,16,6,center)./sqrt(n); % Take USFFT
    y = repmat(w(:),boxcnt,1) .* y; % Tapering
  end