# [R] Fourier Analysis and Curve Fitting in R

stephen sefick ssefick at gmail.com
Tue Jan 29 03:19:05 CET 2008

```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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--
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so little or so large that all they really do for us is puff us up and
make us feel like gods.  We are mammals, and have not exhausted the
annoying little problems of being mammals.

-K. Mullis

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