Amplitude modulation :   AM

f[w_, t_, 
        e_]   =  Sin[(w - e) 
            t] + Sin[(w + e) t]

Plot[f[100, t, 2], {t, 0, 3}, PlotPoints -> 1000]

f[w, t, e] // FullSimplify

now let' s make a discretely sampled
times series

npoints  =  1000;
tmax  =  5;
dt  =  5. /npoints;

timeseries  =  Table[f[100, i dt, 5], {i, npoints}];

ListPlot[timeseries]

    ListPlot[timeseries, PlotJoined -> True]

ListPlot[Abs[Fourier[timeseries]]]

ListPlot[Abs[Fourier[timeseries]], PlotRange -> All]

ListPlot[Abs[Fourier[timeseries]], 
      PlotRange -> {{0, 200}, {0, 10}}]

More points

npoints  =  20000;
tmax  =  5. ;
dt  =  tmax/npoints;
timeseries  =  
        Table[f[100, i dt, 5], {i, npoints}];
ListPlot[Abs[Fourier[timeseries]], 
      PlotRange -> {{50, 125}, All}]
ListPlot[Abs[Fourier[timeseries]], PlotRange -> {{50, 125}, All}, 
      PlotJoined -> True]

dt

fmax  =  1/(2 dt)

df  =  2 fmax / npoints

f  =  
        Table[2  Pi i df, {i, npoints}];
ft  =  Abs[Fourier[timeseries]];
data  =  Table[{f[[i]], ft[[i]]}, {i, 2000}];

ListPlot[data, PlotRange -> {{50, 150}, {0, 30}}, 
      PlotJoined -> True]

f  =  
        Table[2  Pi i df, {i, npoints}];
ft  =  
        10 Log[Abs[Fourier[timeseries]]];
data  =  
        Table[{f[[i]], ft[[i]]}, {i, 
            2000}];
ListPlot[data, PlotRange -> {{50, 150}, All}, 
      PlotJoined -> True]