data1  =  
      Table[Sign[-0.8 + Sin[10*2*Pi*i/256]*Sin[10*2*Pi*j/256]], 
         {i,  0,  256},  {j,  0,  256}];

ListDensityPlot[data1,  Mesh  ->  False];

data2 = Abs[Fourier[data1]];

data3 = 
      Transpose[
        Join[data2[[Range[129, 257],  Range[1, 257]]], 
          data2[[Range[1, 128],  Range[1, 257]]]]];

data4 = 
      Transpose[
        Join[data3[[Range[129, 257],  Range[1, 257]]], 
          data3[[Range[1, 128],  Range[1, 257]]]]];

ListDensityPlot[data4,  PlotRange  ->  {0, 20},  
      Mesh  ->  False];