       Re: Interpolation and plot doing strange things with mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg88999] Re: Interpolation and plot doing strange things with mathematica
• From: ratullochjk2 at gmail.com
• Date: Fri, 23 May 2008 03:08:19 -0400 (EDT)
• References: <g134je\$m3l\$1@smc.vnet.net> <g13h8u\$qo6\$1@smc.vnet.net>

```On May 22, 12:18 am, Jens-Peer Kuska <ku... at informatik.uni-leipzig.de>
wrote:
> 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
>
> ratulloch... 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

can anyone recommend a work around while still keeping the output in
the format as sin and cos or is this not possible?
tia sal2

```

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