function [ PDF_MxM_matrix, range ] = ComputeMxMPDF( coefficients, step_size, M );

coefficients = round( coefficients./step_size );

value_min = min( min( coefficients ) );
value_max = max( max( coefficients ) );

[ row_max, col_max ] = size( coefficients );

PDF_MxM_matrix = zeros( M.^2, value_max - value_min + 1 );

for row_offset = 1:M
  for col_offset = 1:M
    PDF = zeros( 1, value_max - value_min + 1 );
    for row = row_offset:M:row_max
     for col = col_offset:M:col_max
       PDF( coefficients( row, col ) - value_min + 1 ) = PDF( coefficients( row, col ) - value_min + 1 ) + 1;
      end
    end
    PDF_MxM_matrix( (row_offset-1)*M+col_offset, : ) = PDF;
  end
end

PDF_MxM_matrix = PDF_MxM_matrix./(prod(size(coefficients))/M.^2);
range = [ min( min( coefficients ) ), max( max( coefficients ) ) ];