Show[
Plot[{, Sin[x]+(1/2) Sin[3x]},{x,0,10},Axes->False],
DiscretePlot[ Sin[x]+(1/2) Sin[3x],{x,0,10,.5}]
]

points=Table[Sin[.8 2π x],{x,5}];
fit=FindFit[points,A1 Sin[ω1 x+ϕ1]+A2 Sin[ω2 x+ϕ2],{A1,ω1,ϕ1,A2,ω2,ϕ2},x];
fitFn[x_]:=A1 Sin[ω1 x+ϕ1]+A2 Sin[ω2 x+ϕ2] /.fit

Show[
Plot[{, Sin[.8 2π x],fitFn[x]},{x,0,5},Axes->False],
DiscretePlot[ Sin[.8 2π x],{x,0,5,1}]
]

Plot[Sin[x]+(2/3)Sin[3x+1]+(1/4)Sin[5x+2],{x,0,12},Axes->False]

points=N[#,4]&/@Table[Sin[x]+(2/3)Sin[3x+1]+(1/4)Sin[5x+2],{x,0,2π,((2π)/300)}];

dft=Fourier[points];

ListLinePlot[Transpose[{
Range[0, ((1/(2 π/300))), (1/(2 π/300))/(Length[dft] - 1)],
 ((Abs[dft])/(Max[Abs[dft]]))
}]
,PlotRange->{{0,2},All},
Ticks->{{(1/(2π)),(3/(2π)),(5/(2π))},{1,(2/3),(1/4),0}},
GridLines->{{(1/(2π)),(3/(2π)),(5/(2π))},{1,(2/3),(1/4)}},
AxesStyle->White,
GridLinesStyle->Thick]