a1 = 14; a2  =  7; a3  =  4.3;  a4  = 10.2;  A1 = 0.4;  
    A2 = 0.1;  A3  =  0.3;  A4  =  0.4;
data = 
        Table[N[A1*Sin[2*Pi*n/a1] + A2*Sin[2*Pi*n/a2] + A3*Sin[2*Pi*n/a3] + 
              A4*Sin[2*Pi*n/a4]],  {n, 256}];

ListPlot[ data,  PlotJoined  ->  True ]

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