function [Y K] = fftk(X,n,dim)
% [Y K] = fftk(X,n,dim)
%
% FFT performs a Discrete Fourier Transform (DFT) on X and provides, in
% addition, the associated normalized frequencies, K. The DFT is computed
% using MATLAB's fft() command.
%
% Inputs: X - Matrix of input data
% n - [OPTIONAL] FFT(X,n) provides n-point FFT
% dim - [OPTIONAL] Dimension to perform FFT on
%
% Outputs: Y - Matrix of output data
% K - Normalized frequencies corresponding to data
% (Non-singleton dimension will be along dim)
%
% Copyright (c) 2011, Hidden Solutions, LLC
% All rights reserved.
%
% Redistribution and use in source and binary forms, with or without
% modification, are permitted provided that the following conditions are met:
%
% * Redistributions of source code must retain the above copyright
% notice, this list of conditions and the following disclaimer.
% * Redistributions in binary form must reproduce the above copyright
% notice, this list of conditions and the following disclaimer in the
% documentation and/or other materials provided with the distribution.
% * Neither the name Hidden Solutions, LLC nor the names of any
% contributors may be used to endorse or promote products derived from
% this software without specific prior written permission.
%
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
% ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
% WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
% DISCLAIMED. IN NO EVENT SHALL HIDDEN SOLUTIONS, LLC BE LIABLE FOR ANY
% DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
% (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
% LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
% ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
% (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
% SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
%
% Author: James S. Hall (Hidden Solutions, LLC)
% Date: 10 August 2011
%
% Determine size of X
Xsize = size(X);
% Assign dim if not provided
if nargin < 3
dim = find(Xsize>1,1,'first');
if isempty(dim)
dim = 1;
end
end
% Assign n if not provided
if nargin < 2
n = Xsize(dim);
end
% FFT of X
Y = fft(X,n,dim);
% Normalized frequencies
Ksize = ones(1,length(Xsize));
Ksize(dim) = n;
K = zeros(Ksize);
K(:) = (0:n-1)/n;
K(K>=1/2) = K(K>=1/2) - 1;
end