%% NCL ezfftf example 1

x  = [1002, 1017, 1018, 1020, 1018, 1027,...
            1028, 1030, 1012, 1012,  982, 1012,...
            1001,  996,  995, 1011, 1027, 1025, ...
            1030, 1016,  996, 1006, 1002,  982  ];

% mean of x        
xbar = mean(x);
disp(['Mean of x = ' num2str(xbar)])

% number of data points
N = length(x);
disp(['Number of data points: ' num2str(N)])

% compute fft
cf = fft(x-xbar);

% normalize to match NCL - divide by N/2
cf = cf/(N/2);


disp('====================================')
disp('Matlab returns positive and negative frequencies!')
disp('Negative frequencies complex conjugates of positive frequencies.')
disp('First entry is the mean.')
disp('====================================')
% grab the last N/2 entries
cf0 = real(cf(end:-1:13));
cf1 = imag(cf(end:-1:13));
disp('Entries N to N/2')
disp(['Real part: '])
cf0'
disp(['Imaginary part: '])
cf1'

disp('====================================')
% grab the first N/2 entries
disp('Entries 1 to N/2')
cf0 = real(cf(1:12));
cf1 = imag(cf(1:12));

disp(['Real part: '])
cf0'
disp(['Imaginary part: '])
cf1'