[R] Fourier Transform with irregularly spaced x

[Claudia Beleites]

>  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