%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   Blue Noise Generation with MATLAB Implementation   %
%                                                      %
% Author: M.Sc. Eng. Hristo Zhivomirov        07/31/13 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function y = bluenoise(m, n)

% function: y = bluenoise(m, n)
% m - number of matrix rows
% n - number of matrix columns
% y - matrix with blue noise samples 
%     with mu = 0 and sigma = 1 (columnwise)

% The function generates a matrix of blue noise samples
% (columnwise). In terms of power at a constant bandwidth, 
% blue noise increase in at 3 dB/oct, i.e. 10 dB/dec.

% difine the length of the noise vector and ensure  
% that M is even, this will simplify the processing
m = round(m); n = round(n); N = m*n;
if rem(N, 2)
    M = N+1;
else
    M = N;
end

% generate white noise sequence
x = randn(1, M);

% FFT
X = fft(x);

% prepare a vector with frequency indexes 
NumUniquePts = M/2 + 1;     % number of the unique fft points
k = 1:NumUniquePts;         % vector with frequency indexes 

% manipulate the left half of the spectrum so the PSD
% is proportional to the frequency by a factor of f, 
% i.e. the amplitudes are proportional to sqrt(f)
X = X(1:NumUniquePts);  
X = X.*sqrt(k);

% prepare the right half of the spectrum - a conjugate copy of the left
% one except the DC component and the Nyquist component - they are unique,
% and reconstruct the whole spectrum
X = [X conj(X(end-1:-1:2))];

% IFFT
y = real(ifft(X));

% ensure that the length of y is N
y = y(1, 1:N);

% form the noise matrix and ensure unity standard 
% deviation and zero mean value (columnwise)
y = reshape(y, [m, n]);
y = bsxfun(@minus, y, mean(y));
y = bsxfun(@rdivide, y, std(y));

end