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Re: Derivative of experimental data

• To: mathgroup at smc.vnet.net
• Subject: [mg124720] Re: Derivative of experimental data
• From: Armand Tamzarian <mike.honeychurch at gmail.com>
• Date: Thu, 2 Feb 2012 04:56:16 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jgauad$eq8$1@smc.vnet.net>

On Feb 1, 7:49 pm, Gabriel Landi <gtla... at gmail.com> 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.
>
> 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

taking the numerical derivative of experimental data is a noisy
process just as the reverse, integrating, is a smoothing process. that
is the way it is.

incidentally there is a Savitzky-Golay in the wolfram library but it
seems no one ever goes there now to search for code.

Mike