Interpolation and plot doing strange things with mathematica 6 tia
ratull...@gmail.com
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
Jens-Peer Kuska
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
ratull...@gmail.com
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
>
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
Jens-Peer Kuska
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
Daniel Lichtblau
> On May 22, 12:18 am, Jens-Peer Kuska <ku...@informatik.uni-leipzig.de>
> wrote:
>
>>
>>if you make a approximation based on a Fourier series
>>it converges "in the middle" and never point wise
>>
>>Regards
>> Jens
>>
> the format as sin and cos or is this not possible?
> tia sal2
This may be a bit better behaved, numerically. Use a different
integration dummy variable for your Fourier series
<< "FourierSeries`"
s1[x_] = FourierTrigSeries[f[x], y, 25,
FourierParameters -> {-1, 1/138}];
s[x_Real] := Block[{y}, (s1[y] /. Integrate -> NIntegrate) /. y -> x]
Now s[0.] and s[138.] give 2.0, as desired.
In[124]:= s[0.]
Out[124]= -2.
In[125]:= s[138.]
Out[125]= -2.
Daniel Lichtblau
Wolfram Research
Mirek
wrote:
> Hi,
>
> from the point of signal processing not. But you can try to
> use a spline interpolation that has not the tendency to
> oscillate
^^^^^^^^
It has either but differently - short oscillation, higher overshot: