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Derivative of experimental data

  • To: mathgroup at smc.vnet.net
  • Subject: [mg124696] Derivative of experimental data
  • From: Gabriel Landi <gtlandi at gmail.com>
  • Date: Wed, 1 Feb 2012 03:48:04 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Dear MathGroup users,

I have a question which is very important for my current research, and 
which involves not only Mathematica, but computer science in general.

I have experimental data which is not very noisy, a small example of 
which may be downloaded here. 

Basically I need to compute the derivative of this data. Here are my 
options so far:

Option 1: Finite differencing. Its terrible since the noise enhances 
dramatically.
Option 2: Fitting some arbitrary function. The problem is that the 
general functional form of the data changes from experiment to 
experiment, so it is not possible to find a function which fits 
adequately in all cases.
Option 3: Savitzky-Golay filters (self-implemented in Mathematica, based 
on the discussion in Numerical Recipes, 3rd Ed.). It doesn't seem to 
make much of a difference; probably because my data is not really that 
noisy.
Option 4: Smoothing Splines filter. I am currently using Mr. Ludsteck 
package HPFilter. So far it is by far the best outcome. However, it is 
not free of some wild oscillations that are clearly non-analytical and 
which are giving me quite the headache.

Any suggestions are more than welcome.
I really appreciate any help I can get.

Best regards,

Gabriel Landi


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