# [R] Fourier Analysis and Curve Fitting in R

Carson Farmer cfarmer at uvic.ca
Tue Jan 29 00:10:38 CET 2008

```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
>>

```