data7  =  
      Table[Sign[-0.9 + Sin[10*2*Pi*i/128]*Sin[10*2*Pi*j/128]], 
         {i,  0,  128},  {j,  0,  128}];

ListDensityPlot[data7,  Mesh  ->  False];

data8 = Fourier[data7];

ListDensityPlot[Abs[data8],  PlotRange  ->  {0, 4},  
      Mesh  ->  False];

data9 = Abs[data8];

ListDensityPlot[data9[[ Range[1, 64],  Range[1, 64]]],  
      PlotRange  ->  {0,  4},  Mesh  ->  False];

data10 = data9[[ Range[1, 64],  Range[1, 129]]];

data11 = data9[[ Range[65,  129],  Range[1,  129]]];

ListDensityPlot[Join[data11, data10],  PlotRange  ->  {0, 4},  
      Mesh  ->  False];

data12 = Transpose[Join[data11,  data10]];

ListDensityPlot[data12,  PlotRange  ->  {0, 4},  
      Mesh  ->  False];

data13 = data12[[ Range[1, 64],  Range[1, 129]]];

data14 = data12[[ Range[65,  129],  Range[1,  129]]];

finalone  =  Transpose[Join[data14,  data13]];

ListDensityPlot[finalone,  PlotRange  ->  {0, 4},  
      Mesh  ->  False];