olekravchenko

(*FDE:
f'(x) = 2.25*(3f(3x) - 2f(3x-1) - f(3x-2)),
supp f = [0,1]
*)
(*Fourier Transform of f(x)*)
fFt[\[Omega]_] := 
 Product[1/4 (3 - 2 Exp[-I \[Omega] 3^-n] - Exp[-2 I \[Omega] 3^-n])/(
   I \[Omega] 3^-n), {n, 1, 4}]
(*Fourier Series of f(x)*)
f[x_] := 0.5 + 

olekravchenko

(*Fabius Function*)
Fb[x_] := up[x - 1, 5, 30]
(*Statement Function*)
GFb[a1_, a2_, b_] := a2 - a1 + b (Fb[a1/b] - Fb[a2/b]) // Evaluate
(*Samples*)
GFb[2, 13, 30];
GFb[2, 7, 18];

(*Search*)
tbl = Table[{b, GFb[2, 9, b]}, {b, 15, 25, 1}];

olekravchenko

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},