[R] Fourier Transform with irregularly spaced x
Claudia Beleites
cbeleites at units.it
Mon Nov 3 17:01:07 CET 2008
> 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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