       Re: Interpolation and plot doing strange things with mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg88978] Re: Interpolation and plot doing strange things with mathematica
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 22 May 2008 06:16:59 -0400 (EDT)
• Organization: Uni Leipzig
• References: <g134je\$m3l\$1@smc.vnet.net>

```Hi,

if you make a approximation based on a Fourier series
it converges "in the middle" and never point wise
The most famous example is the Gibbs phenomenon.
http://en.wikipedia.org/wiki/Gibbs_phenomenon

Regards
Jens

ratullochjk2 at gmail.com wrote:
> Greetings All
>
> I run these commands that I've had plenty of help getting to
> work...but the plot doesn't follow the points, as you can see in the
> plot.  At the end it just goes crazy and when I test the points with
>
> input s
> output is -3.73293
> why are the numbers so out of sync... at s it should be -2 not
> -3.73293
>
> I try increasing the number in the line
> N[FourierTrigSeries[f[x], x, 25, FourierParameters -> {-1, 1/138}]]
> (I've changed the number 25 to over 100 and the problem seems to get
> worse)
>
> See code below:
>
> In:= data3 = {{0, -2}, {7, 1}, {10, 6}, {12, -2}, {18, -6}, {27,
> 6}, {34,
>     4}, {42, -6}, {49, -5}, {56, 4}, {62, 3}, {67, -5}, {70, -3}, {79,
>      3}, {83, 7}, {88, -3}, {89, -8}, {96, 7}, {105,
>     9}, {113, -8}, {122, -9}, {131, 9}, {132,
>     1}, {134, -9}, {138, -2}};
> f = Interpolation[data3, PeriodicInterpolation -> True];
>
> << "FourierSeries`"
>
> s[x_] = N[
>   FourierTrigSeries[f[x], x, 25, FourierParameters -> {-1, 1/138}]]
>
> discr = Interpolation[data3 /. {x_, y_} -> {x, y},
>    InterpolationOrder -> 1];
>
> g[x_] = Piecewise[{{discr[x], 0 < x < 138}, {0, True}}];
>
> Show[Plot[s[x], {x, 0, 138}, PlotStyle -> Red,
>   PlotRange -> {-15, 15}], Plot[g[x], {x, 0, 138}, Filling -> Axis],
>  ListPlot[data3, Filling -> Axis, PlotRange -> {0, 138}]]
>
> tia sal2
>

```

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