a1 = 20; a2  =  7; A1 = 1.0;  A2 = 0.1;
data = 
        Table[N[A1*Sin[2*Pi*n/a1] + A2*Sin[2*Pi*n/a2]],  {n, 
            256}];

ListPlot[ data,  PlotJoined  ->  True ]

spec = Abs[Fourier[data]];
ListPlot[spec[[Range[1, 128]]],  PlotJoined  ->  True,  
      PlotRange  ->  All ]