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Re: Derivative of experimental data

  • To: mathgroup at smc.vnet.net
  • Subject: [mg124738] Re: Derivative of experimental data
  • From: Matthias Odisio <matthias at wolfram.com>
  • Date: Fri, 3 Feb 2012 02:10:54 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201202010848.DAA15135@smc.vnet.net>

Dear Gabriel,

On 2/1/12 2:48 AM, Gabriel Landi wrote:
> 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. 
> 

Would you like to share some of these data with us?


> 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


How do these functions perform on your data?

DerivativeFilter

GaussianFilter (smoothing + derivation)
TotalVariationFilter, WienerFilter (smoothing, for pre-processing)


Matthias Odisio
Wolfram Research




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