Dirac comb

(*start*)
(*Dirac comb Fourier series*)
ListLinePlot[
 Table[Sum[Cos[x*(k)/NN*2*Pi], {k, 1, NN}], {x, 0, xmax, 0.1}],
 PlotRange -> {-4, NN + 1/2}]
(*end*)


(*Mathematica*)
(*program start*)
Clear[x, y, n, a, xmin, xmax, ymin, ymax, c]
xmin = -3*Pi;
xmax = +3*Pi;
x = N[Range[xmin, xmax, 1/(50*Pi)], 90];
y1 = Cos[x] - 1;
y2 = Sin[y1];
y3 = Sin[y1 + y2];
y4 = Sin[y1 + y2 + y3];
y5 = Sin[y1 + y2 + y3 + y4];
y6 = Sin[y1 + y2 + y3 + y4 + y5];
y7 = Sin[y1 + y2 + y3 + y4 + y5 + y6];
y8 = Sin[y1 + y2 + y3 + y4 + y5 + y6 + y7];
y9 = Sin[y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8];
y10 = Sin[y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8 + y9];
y11 = Sin[y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8 + y9 + y10];
y12 = Sin[y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8 + y9 + y10 + y11];
y = y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8 + y9 + y10 + y11 + y12;
Max[y]
a = Table[{x[[n]], Pi + y[[n]]}, {n, 1, Length[x]}];
a1 = Table[{x[[n]], Pi + y1[[n]]}, {n, 1, Length[x]}];
a2 = Table[{x[[n]], Pi + y2[[n]] + y1[[n]]}, {n, 1, Length[x]}];
a3 = Table[{x[[n]], Pi + y3[[n]] + y2[[n]] + y1[[n]]}, {n, 1,
    Length[x]}];
a4 = Table[{x[[n]], Pi + y4[[n]] + y3[[n]] + y2[[n]] + y1[[n]]}, {n,
    1, Length[x]}];
a5 = Table[{x[[n]],
    Pi + y5[[n]] + y4[[n]] + y3[[n]] + y2[[n]] + y1[[n]]}, {n, 1,
    Length[x]}];
a6 = Table[{x[[n]],
    Pi + y6[[n]] + y5[[n]] + y4[[n]] + y3[[n]] + y2[[n]] +
     y1[[n]]}, {n, 1, Length[x]}];
a7 = Table[{x[[n]],
    Pi + y7[[n]] + y6[[n]] + y5[[n]] + y4[[n]] + y3[[n]] + y2[[n]] +
     y1[[n]]}, {n, 1, Length[x]}];
a8 = Table[{x[[n]],
    Pi + y8[[n]] + y7[[n]] + y6[[n]] + y5[[n]] + y4[[n]] + y3[[n]] +
     y2[[n]] + y1[[n]]}, {n, 1, Length[x]}];
a9 = Table[{x[[n]],
    Pi + y9[[n]] + y8[[n]] + y7[[n]] + y6[[n]] + y5[[n]] + y4[[n]] +
     y3[[n]] + y2[[n]] + y1[[n]]}, {n, 1, Length[x]}];
a10 = Table[{x[[n]],
    Pi + y10[[n]] + y9[[n]] + y8[[n]] + y7[[n]] + y6[[n]] + y5[[n]] +
     y4[[n]] + y3[[n]] + y2[[n]] + y1[[n]]}, {n, 1, Length[x]}];
a11 = Table[{x[[n]],
    Pi + y11[[n]] + y10[[n]] + y9[[n]] + y8[[n]] + y7[[n]] + y6[[n]] +
      y5[[n]] + y4[[n]] + y3[[n]] + y2[[n]] + y1[[n]]}, {n, 1,
    Length[x]}];
a12 = Table[{x[[n]],
    Pi + y12[[n]] + y11[[n]] + y10[[n]] + y9[[n]] + y8[[n]] +
     y7[[n]] + y6[[n]] + y5[[n]] + y4[[n]] + y3[[n]] + y2[[n]] +
     y1[[n]]}, {n, 1, Length[x]}];
ymin = Min[y]/Pi;
ymax = Max[y]/Pi;
ymin = -10/2*Pi;
ymax = 10/2*Pi;

g = ListLinePlot[a,
   Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
     Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
   ImageSize -> Full, PlotRange -> {-1/2, Pi + 1/2}];
g1 = ListLinePlot[a1,
   Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
     Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
   ImageSize -> Full, PlotRange -> {-1/2, Pi + 1/2}];
g2 = ListLinePlot[a2,
   Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
     Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
   ImageSize -> Full, PlotRange -> {-1/2, Pi + 1/2}];
g3 = ListLinePlot[a3,
   Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
     Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
   ImageSize -> Full, PlotRange -> {-1/2, Pi + 1/2}];
g4 = ListLinePlot[a4,
   Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
     Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
   ImageSize -> Full, PlotRange -> {-1/2, Pi + 1/2}];
g5 = ListLinePlot[a5,
   Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
     Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
   ImageSize -> Full, PlotRange -> {-1/2, Pi + 1/2}];
g6 = ListLinePlot[a6,
   Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
     Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
   ImageSize -> Full, PlotRange -> {-1/2, Pi + 1/2}];
g7 = ListLinePlot[a7,
   Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
     Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
   ImageSize -> Full, PlotRange -> {-1/2, Pi + 1/2}];

g8 = ListLinePlot[a8,
   Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
     Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
   ImageSize -> Full, PlotRange -> {-1/2, Pi + 1/2}];

g9 = ListLinePlot[a9,
   Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
     Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
   ImageSize -> Full, PlotRange -> {-1/2, Pi + 1/2}];

g10 = ListLinePlot[a10,
   Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
     Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
   ImageSize -> Full, PlotRange -> {-1/2, Pi + 1/2}];

g11 = ListLinePlot[a11,
   Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
     Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
   ImageSize -> Full, PlotRange -> {-1/2, Pi + 1/2}];

g12 = ListLinePlot[a12,
   Ticks -> {Flatten[{xmin, xmax, Table[n, {n, xmin, xmax, Pi}]}],
     Flatten[{ymin, ymax, Table[k, {k, ymin, ymax, Pi}]}]},
   ImageSize -> Full, PlotRange -> {-1/2, Pi + 1/2}];

Show[g, g1, g2, g3, g4, g5, g6, g7, g8, g9, g10, g11, g12]
Show[g10]
(*program end*)