[Ifeffit] Re: Independent data poins in Artemis
Scott Calvin
SCalvin at slc.edu
Thu Jan 4 14:57:29 CST 2007
Thanks, Jeremy. Good point.
As a practical matter, what you actually get when a Fourier transform
algorithm is applied to a data set consisting of a single point will
depend on the algorithm. If the algorithm pads with 0's, it gets a
transform that starts to look more and more "white," that is, like a
constant function in transform space. If it doesn't pad with 0's, but
instead takes the usual Fourier integral and let the limits of
integration tend toward 0, so that it only includes the non-zero
point, the transform approaches a delta function located at 0 in
transform space. Those results are as different as they could be, and
they depend entirely on how the truncation is handled. (A typical
ifeffit calculation, as I understand it, lies between these two
extremes. It integrates over a finite interval, but pads with 0's to
get to a convenient number of points.) I think that nicely
demonstrates that you can't extract information from the "Fourier
transform" of a single point.
--Scott Calvin
Sarah Lawrence College
At 03:20 PM 1/4/2007, you wrote:
>Rigorously speaking, a single point is not a delta function. To have a
>delta function, only one point has a non-zero value, all other points
>are zero. If you have only one data point and you assume all other
>points are zero, you are adding information not contained in your data.
>
>Jeremy Kropf
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