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Re: How does one get data out of a TemporalData object?

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  • Subject: [mg131209] Re: How does one get data out of a TemporalData object?
  • From: Joe Gwinn <joegwinn at comcast.net>
  • Date: Mon, 17 Jun 2013 06:29:12 -0400 (EDT)
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  • References: <20130615082528.D46F866F8@smc.vnet.net> <kpjvbv$9mc$1@smc.vnet.net>

In article <kpjvbv$9mc$1 at smc.vnet.net>, Andy Ross <andyr at wolfram.com>
wrote:

Andy,

> TemporalData has a number of properties for extracting the parts you 
> need. To get the paths with time stamps use TemporalData[...]["Paths"]. 
> To get the states use TemporalData[...]["States"].
> 
> I recommend looking at the details section of the documentation for 
> TemporalData to see the full list of properties and read through the 
> examples on that page to see how each is used.

I had looked over the documentation, and nothing jumped out.  I looked
at every mention of TemporalData, and found nothing that seemed
suitable.  

But I didn't try States, so I just did. It yields a list of alternating
1 and 2 values, which isn't a complete answer to the problem, as the
time values are missing.  If one just uses Fourier[], one will get some
kind of Periodogram, which is not what is sought.

Let me give a code example:

\[ScriptCapitalP] = ContinuousMarkovProcess[{1, 0}, ({
     {-3, 3},
     {1, -1}
    })];
data=RandomFunction[\[ScriptCapitalP],{0,20}]
Fourier[data]

This yields a complaint:
Fourier::fftl: 
(((((("\"Argument \!\(\*TagBox[\nRowBox[{\\\"TemporalData\\\",
\\\"[\\\", PanelBox[" 1) ", FrameMargins->Small], \\\"]\\\"}],
InterpretTemplate[TemporalData[Automatic, {{{1, 2, 1, 2, 1, 2, 1, 2, 1,
2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1}}, {{{0``15.954589770191005,
0.01520207123587128013320057817736596917`14.129940038322594,
0.95824522046395536932862513249273766604`15.644199356725549,
1.53128564596308252148382664967984035205`15.736304825316484,
2.28962713530000690099771260582537312886`15.797207858258304,
3.28670141416927664988333023187555326092`15.839226787640209,
3.38168097695521799981621844019305806672`15.842081650549387,
4.0716904019295301685379386805431332727`15.859211783981653,
5.25370702200219072713176547011226038622`15.878918089214274,
5.91828379716574832280816964564910319058`15.88678718369098,
6.12633788645240157414249230434964341735`15.888924305967711,
6.19666658844600659408879868858704605186`15.889616516866917,
9.58526332575202981025003709494096121015`15.911492152203763,
9.8441361181069966832633195553354003832`15.912572420088354,
14.33613695082054447978910756738149487066`15.925305933162454,
14.96549983870748084202749476200455050281`15.926498477053611,
15.17014786638371663403108748271496533041`15.92686559286194,
15.36161929373388768828517022927544623659`15.927200484830422,
15.67573549317739061376647722217804251544`15.927732699101226,
15.8362986262877527919959498312816012794`15.927996832624787,
16.94396941821241069345266065715083372759`15.929686408696478,
17.04737697478590359190098510749722701209`15.929833245160726,
22.73457835309395939446096043959096018021`15.93589515332067}}}, 1, {")
Discrete) ", 1}, {") Continuous) ", 1}, 1, {}}]& ], Editable->False,
SelectWithContents->True, Selectable->True]\) is not a non-empty list
or rectangular array of numeric quantities.\"")

Now, note that the following appears to work:

plot1 = ListLinePlot[data, InterpolationOrder -> 0, 
  PlotRange -> {1, 2.1}, Ticks -> {Automatic, {1, 2, 3}}, 
  Filling -> Bottom]

But when I do this:

datainter = 
 Interpolation[Normal[data] // First, InterpolationOrder -> 0]
plot2 = Plot[datainter[t], {t, 0, 20}, PlotRange -> All, 
  Filling -> Bottom]

I get a different answer, and other paths yield yet other answers.


What I'm looking for is for instance a function that can be called from
Table[] to yield a list of equispaced samples suitable for Fourier[]. 
The locations and interval between samples may vary as needed to keep
Fourier happy - list length will be an exact power of two, and there
may be zero padding added.

Thanks,

Joe Gwinn


> Andy Ross
> Wolfram Research
> 
> On 6/15/2013 3:25 AM, Joe Gwinn wrote:
> > I would like to generate some random signals for use in exploring
> > signal-processing algorithms.
> >
> > For use as synthetic signals for the algorithm to chew upon, I'd like
> > to use ContinuousMarkovProcess and TelegraphProcess with
> > RandomFunction.  With these, I can do statistics and plot things
> > freely.
> >
> > What I cannot quite get is a time series ready for such indignities as
> > Fourier[].
> >
> > Now I can manually disassemble the data structure, but I don't find a
> > list of equispaced samples, I get a transition list, which is not the
> > same thing.
> >
> > Interpolation[Normal[temporal data object] // First, InterpolationOrder
> > -> 0] almost works, but the fine details are smeared over, even though
> > InterpolationOrder -> 0 works in ListLinePlot et al without apparent
> > smearing.
> >
> > What am I missing?  It seems like Probability and Statistics has become
> > a walled city within Mathematica.  I'm hoping to find a door in the wall,
> > rather than be forced to build by own little city one brick at a time.
> >
> > Joe Gwinn
> >
> 
>



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