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

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  • Subject: [mg131227] Re: How does one get data out of a TemporalData object?
  • From: Andy Ross <andyr at wolfram.com>
  • Date: Wed, 19 Jun 2013 01:27:10 -0400 (EDT)
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  • References: <20130615082528.D46F866F8@smc.vnet.net> <kpjvbv$9mc$1@smc.vnet.net> <20130617102912.3DFA76A92@smc.vnet.net>

Does the following do what you want?

Plot[data["SliceData", t], {t, 0, 20}, Filling -> Bottom]

The "SliceData" property performs the same interpolation as ListLinePlot 
in this case (can be controlled via Method option) and returns 
time-value pairs.

-Andy

On 6/17/2013 5:29 AM, Joe Gwinn wrote:
> 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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