Created
April 28, 2016 05:30
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up.nb
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| FTup[x_, elemProd_] := Product[Sinc[x 2^-k], {k, 1, elemProd}] | |
| up[x_, elemProd_, elemSum_] := | |
| If[-1 <= x && x <= 1, | |
| 0.5 + Sum[FTup[k \[Pi], elemProd] Cos[\[Pi] k x], {k, 1, elemSum}], | |
| 0] | |
| elemProd = 4; | |
| elemSum = 20; | |
| Plot[{up[x, elemProd, elemSum]}, {x, -1 - 0.025, 1 + 0.025}, | |
| PlotRange -> Full, PlotStyle -> Thick, | |
| PlotLabel -> Text[Style["up(x) function", 12]], Filling -> Axis, | |
| ImageSize -> 640] |
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Computation of atomic up(x) function (first prime of Fabius function) by Fourier cosine series approximation (since up(x) is even function).