a1 = 20; a2  =  7; A1 = 1.0;  A2 = 0.5; 
    A3 = 0.2;
data = 
        Table[N[A1*Sin[2*Pi*n/a1] + A2*Sin[2*Pi*n/a2] + 
              A3*(Random[]  -  0.5)],  {n, 256}];

ListPlot[ data,  PlotJoined  ->  True ]

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