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Reverseengineer fractal resampling process 
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#1
Jun3014, 11:24 PM

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Hey,
I am working on a project where I need to take several time series of various lengths and identify common features. So, for example, a period of 100 days may exhibit the same features as a period of 10 days  the system is selfsimilar in this way. In order to compare these series of different lengths I need to strip out noise that is not important for feature identification in order to bring them to the same scale. I have come across this document that shows a rather efficient method of doing this and would like to reverse engineer it... any help greatly appreciated. http://www.congrexprojects.com/docs/...resampling.pdf 


#2
Jul114, 11:35 AM

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#3
Jul114, 04:14 PM

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P: 7,175

Doesn't page 8 already explain it?
If the original data set is ##x_0, x_1, \dots##, start by keeping the points ##x_0, x_{2^k}, 2x_{2^k}, \dots## for a "large" value of ##k##. If linear interpolation between those points is not good enough in an interval, add the midpoint of that interval to the list of points. Rinse and repeat till the result is accurate enough. In the example they start from ##x_0## and ##x_8##, then add the mid point ##x_4##, etc. You might want to compare this will something like spline fitting adaptive knot placement, e.g. http://www3.stat.sinica.edu.tw/stati...pdf/A20n39.pdf For the "inspiration" on page 7, google fractal (or fractional) brownian terrain generation. 


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