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From: Jerry Avins <jya@ieee.org>
Newsgroups: comp.dsp,comp.soft-sys.matlab
Subject: Re: DFT of an irregular time-spacing signal
Date: Tue, 22 Oct 2002 14:06:59 -0400
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Ken Davis wrote:
> 
> Hello,
> 
> I believe that there is no simple way to write a DFT for unevenly spaced
> data. The DFT/FFT (they are the same function, but the FFT is a fast
> algorithm for computing the DFT), requires evenly spaced data in it's
> underlying assumptions. If the set of samples is not not evenly spaced,
> then, in general, the spectrum will not be a finite, discrete set of
> frequencies.
> 
> If you take the "naive" approach and just take the inner product of your
> sample vector with a collection of complex sinusoids sampled with the same
> uneven spacing, you will get a set of numbers, but those numbers will not be
> a very good representation of the power spectrum since the unevenly sampled
> sinusoids will not form an orthonormal set.
> 
> HTH,
> 
> Ken
> 
Amen! A simple and stringent test of such a "transform" is the ability
to recreate the original set of points. One could devise a figure of
merit for various interpolation methods that uses closeness to exact
reproduction as its measure. Mean square error seems appropriate.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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