[R] Fourier Transform with irregularly spaced x

[stephen sefick]

neat. I learn something everyday

On Mon, Nov 3, 2008 at 11:01 AM, Claudia Beleites <cbeleites at units.it> wrote:
>>  Try http://finzi.psych.upenn.edu/R/library/nlts/html/spec.lomb.html or
>> http://finzi.psych.upenn.edu/R/library/cts/html/spec.ls.html (do
>> RSiteSearch("Lomb periodogram")  --
>> the Lomb periodogram does a discrete (although not fast) Fourier
>> transform of unevenly sampled (1D/time-series) data, accounting for
>> the sampling distribution of points (which will the bias the results
>> if you try to do a naive Fourier sum).
> Thanks Ben, that looks like a good start point.
>
> Stephen, my aim are neither spline nor linear approximation but something in
> the line of matlab's interpfft
>
> I do have the vibrational spectrum. Such spectra are frequently computed by ft
> from their (measured) interferograms. I.e. if you use an FT-spectrometer.
> However, the spectra can also be measured directly with a dispersive
> instrument. The difference between neighbouring frequencies of such spectra
> varies over the spectrum. E.g. I measure from 600 cm^-1 to 1800 cm^-1: at 600
> cm^-1 I have a data point spacing of 1.04 cm^-1, while at 1800 cm^-1 it is
> only 0.85 cm^-1. So doing a ft (like spec.pgram ()) only on the signal means
> that I do not use periodic functions (sin x), but something rather like sin
> (x^2) - the sinus changes its frequency. This does not help.
>
> The idea is to calculate the interferogram (space or time domain) taking into
> account this variation of delta nu. Then do a backtransform to evenly spaced
> frequencies.
> The next step will then be to do other interesting things like downsampling,
> denoising etc. using the interferogram.
>
> Thanks,
>
> Claudia
>
>
>
> --
> Claudia Beleites
> Dipartimento dei Materiali e delle Risorse Naturali
> Università degli Studi di Trieste
> Via Alfonso Valerio 6/a
> I-34127 Trieste
>
> phone: +39 (0 40) 5 58-34 47
> email: cbeleites at units.it
>
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>



-- 
Stephen Sefick
Research Scientist
Southeastern Natural Sciences Academy

Let's not spend our time and resources thinking about things that are
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