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Re: Interpolation and plot doing strange things with mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg89016] Re: Interpolation and plot doing strange things with mathematica
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Sat, 24 May 2008 03:50:26 -0400 (EDT)
• Organization: Uni Leipzig
• References: <g134je$m3l$1@smc.vnet.net> <g13h8u$qo6$1@smc.vnet.net> <g15qpi$pe9$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de

Hi,

from the point of signal processing not. But you can try to
use a spline interpolation that has not the tendency to
oscillate and resample the data or use the resampled
data for your trigonometric approximation.
I would recommend an Akima spline.
If you don't have a non parametric spline computation
take my http://phong.informatik.uni-leipzig.de/~kuska/NonParametricSplines.zip
package, install it in your Mathematica/Applications/AddOns directory
and have a look into the documentation (DocumentationCenter/Installed 
AddOns).

Regards
   Jens

ratullochjk2 at gmail.com wrote:
> 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[0]
>>> output is -3.73293
>>> why are the numbers so out of sync... at s[0] 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[89]:= 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
>