[Fwd: Fourier Series Expansions and it's Coefficients question

• To: mathgroup at smc.vnet.net
• Subject: [mg85262] [Fwd: [mg85198] Fourier Series Expansions and it's Coefficients question
• From: mante <claude.mante at univmed.fr>
• Date: Tue, 5 Feb 2008 05:54:25 -0500 (EST)

```Hello,
ihis solution looks like your example :

y = {14, 18.7, 9, 4.1, 6.7, 6, 6.3, 8.4, 4, 2.9};
x = Range[0, Length@y];

f[z_] := Piecewise[
Table[{y[[i]], x[[i]] < z < x[[i + 1]]}, {i, Length@y}]];

T = (-First@x + Last@x);
co[n_] = 2 Integrate[f[t] Cos[n 2 \[Pi]  t/T], {t, First@x, Last@x}]/
T;
si[n_] = 2 Integrate[f[t] Sin[n 2 \[Pi]  t/T], {t, First@x, Last@x}]/
T;
A0 = Integrate[f[t] , {t, First@x, Last@x}]/T;
approx[t_] :=
A0 + Sum[co[k] Cos[k 2 \[Pi]  t/T] + si[k] Sin[k 2 \[Pi]  t/T], {k,
10}];

Plot[{f[t], approx[t]}, {t, First@x, Last@x}]

--
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Claude Manté

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