[R] Fourier Analysis and Curve Fitting in R

[Spencer Graves]

The 'fda' package supports fitting finite Fourier series with examples 
in 'canadian-weather.R' and 'gait.R' in the 'demo' subdirectory of 
'~R\library\fda\fda';  see also 'fda-ch01.R' in the 'scripts' 
subdirectory.  Also, the 'percur' funcction in the 'DierckxSpline' 
package supports fitting periodic splines. 

stephen sefick wrote:
> well if you want to find the spectral density aka what frequencies
> explain most of the variance then I would suggest the spectral
> density.  This can be implemented with spec.pgram().  This is
> conducted with the fast fourier transform algorithm.
>   
>> a<-ts(data, frequency = 1)   #make the time series with 365readings/365days
>> ?spec.pgram
>>     
> and you should be able to take it from here
>
> This will give you the raw periodogram and the dominant frequencies
> after you smooth the periodogram.  If your intention is to just fit a
> curve to your data there are many types of cuve fitting options moving
> average etc.
>
> What are you trying to do find the dominant periodicy? make a
> prediction equation? fit a smooth line? or...
>
> give us some more information and maybe we can help
>
>
> On 1/28/08, Carson Farmer <cfarmer at uvic.ca> wrote:
>   
>> Rolf Turner wrote:
>>     
>>>> On 26/01/2008, at 10:54 AM, Carson Farmer wrote:
>>>>
>>>>         
>>>>> Dear List,
>>>>>
>>>>> I am attempting to perform a harmonic analysis on a time series of snow
>>>>> depth, in which the annual curve is essentially asymmetric (i.e. snow
>>>>> accumulates slowly over time, and the subsequent melt occurs relatively
>>>>> rapidly).  I am trying to fit a curve to the data, however, the actual
>>>>> frequency is unknown.
>>>>>           
>>> In general the actual frequency of the curve will indeed be close to
>>> 1/(1 year). However, because I intend to perform this analysis on many
>>> regions, this will not always be the case. This is perhaps an
>>> acceptable assumption however...
>>>       
>>>>     Obviously there is something I am not understanding here.
>>>>     I would have thought that the ``actual frequency'' would
>>>>     be 1/(1 year) (period = 1 year) --- modulo the fact that
>>>>     the length of the year is constantly changing a tiny bit.
>>>>     (But I would've thought that this would have no practical
>>>>     impact in respect of any observed series.)
>>>>
>>>>         
>>> My sampling interval is daily.
>>>       
>>>>     What is your sampling interval, BTW? Day?  Week?  Month?
>>>>         
>>>>> I have been trying to follow the methods in Peter
>>>>> Bloomfields text "Fourier Analysis of Time Series", but am having
>>>>> trouble implementing this in R.
>>>>>           
>>> Yes it certainly would.
>>>       
>>>>     Note that even though the ``actual frequency'' is (???) 1/(1 year),
>>>>     the representation of the mean function in terms of sinusoids
>>>>     will involve in theory infinitely many terms/frequencies since
>>>>     the mean function is clearly (!) not a sinusoid.
>>>>
>>>>         
>>>>> Does anyone have any suggestions, or perhaps directions on how this
>>>>> might be done properly? Am I using the right methods for fitting an
>>>>> asymmetric curve?
>>>>>           
>>> What I am really trying to do is fit a relatively smooth line to my
>>> data which will preferentially weight the larger values. This method
>>> needs to be able to fit through data gaps however, which is why I was
>>> originally looking to fit sinusoids. A jpg of a single year of the
>>> data is available here:
>>> <http://www.geog.uvic.ca/spar/carson/snowDepth.jpg> to give you an
>>> idea of the shape of my curve.
>>> Thank you again for your help,
>>>
>>> Carson
>>>       
>>>>     I would have to know more about what you are *really* trying
>>>>     to do, and what the data are like, before I could make any
>>>>     useful suggestions.  Many modelling issues could come into
>>>>     play, and many modelling strategies are potentially applicable.
>>>>
>>>>         cheers,
>>>>
>>>>             Rolf Turner
>>>>
>>>>         
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>>     
>
>
>