<< Graphics`Graphics`
<< Calculus`FourierTransform`

part 1 : finding components of mixing 3 waves

ft = {2 , 4 Sin[ω t], Cos[2 ω t], 
          2  Sin[6 ω t + 60  °]} /. ω ->  
          2 π 1
zu1 = 
      Plot[{ft[[1]], ft[[2]]}, {t, 0, 1}, 
        GridLines ->  Automatic, AspectRatio ->  0.2, 
        PlotStyle ->  {Hue[0.9], Hue[0.7]}]

zu2 = 
      Plot[{ft[[3]], ft[[4]]}, {t, 0, 1}, 
        GridLines ->  Automatic, AspectRatio ->  0.2, 
        PlotStyle ->  {Hue[0.9], Hue[0.7]}]

wt = ft . {1, 1, 1, 1};
zu3 = 
      Plot[wt, {t, 0, 1}, GridLines ->  Automatic, 
        AspectRatio ->  0.3, PlotStyle -> Hue[0.7]]

Chop[FourierTrigSeries[wt, t, 10]]

part 2 :ex 5.15  approximating of periodic wave  p.82

wt = 2 + 20 t
wtt = 2 + 20 (t - Round[t])
Plot[wtt, {t, -1, 1}, AspectRatio ->  0.3, 
      GridLines ->  Automatic]

f1 = Chop[FourierTrigSeries[wt, t, 1]];
f2 = Chop[FourierTrigSeries[wt, t, 2]];
f15 = Chop[FourierTrigSeries[wt, t, 15]]

Plot[{wtt, f1, f2}, {t, -1, 1}, AspectRatio ->  0.3, 
      GridLines ->  Automatic, 
      PlotStyle ->  {Hue[0.9], Hue[0.7], Hue[0.5]}]

Plot[{wtt, f15}, {t, -1, 1}, AspectRatio ->  0.3, 
      GridLines ->  Automatic, 
      PlotStyle ->  {Hue[0.9], Hue[0.7]}]

tab16 = 
      Flatten[{2, 
          Table[Coefficient[f15, Sin[n 2 π t]], {n, 1, 
              15}]}]
xlabel = Table[n, {n, 0, 15}];

BarChart[Abs[tab16], PlotRange ->  {0, 8}, 
      AspectRatio ->  0.5, BarLabels ->  xlabel, 
      GridLines ->  Automatic]