Il teorema di Shannon

Definiamo la funzione sinc:

sinc[0] = 1

sinc[t_]  :=  Sin[π t]/(π t)

Il segnale da sviluppare in serie di sinc:

x[t_] :=  4 Sin[t/2]^2/t^2

gr1  =  
        Plot[x[t],  {t, -14, 
            14},   PlotStyle -> {Thickness[0.01],  
              RGBColor[1, 0, 0]},  PlotRange -> All];

s[n_, t_] :=  
      Sum[ x[k/2] *sinc[2  t  -  k],  {k, -n, n}] // N

gr10  =  
        Plot[s[10, t],  {t, -14, 14},  
          PlotStyle -> {Thickness[0.005],  RGBColor[0, 0, 1]},  
          PlotRange ->  All];

Show[gr1,  gr10,  ImageSize  -> {450,  300}];

gr20  =  
        Plot[s[20, t],  {t, -14, 14}, 
          PlotStyle -> {Thickness[0.005],  RGBColor[0, 0, 1]},  
          PlotRange ->  All];

Show[gr1,  gr20,  ImageSize  -> {450,  300}];