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Re: getting derivatives from spline [message #66043 is a reply to message #66029]

Mon, 13 April 2009 09:54

jameskuyper
Messages: 79
Registered: October 2007

Member

Jeremy Bailin wrote:
> Does anyone know a way of getting SPLINE or any of its friends to
> return the derivatives of the interpolating function at the desired
> abscissae in addition to the interpolated values?
>
> Or, another way of getting at this question: what is everyone's
> favourite algorithm for numerically calculating the derivatives of
> (slightly) noisy data?

Don't use splines to fit noisy data. The spline treats the noise as
being just as real as the signal. Particularly with higher-order
splines, it's easy to end up with interpolated data which looks even
noisier than the raw data.

Instead, fit the noisy data to a model with fewer free parameters than
you have data points. The difference between the number of data points
and the number of free parameters is a measure of the amount of
information you're discarding. If you've made a good choice of model,
the information you're discarding will be about the noise; with a bad
model, you'll be discarding information about the signal. Choosing the
right model for your data is therefore a key step in this process.

The fundamental problem with using splines is that the number of data
points is the same as the number of free parameters - you aren't
discarding any noise.

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[Message index]

		Re: getting derivatives from spline By: Jeremy Bailin on Tue, 14 April 2009 05:50
		Re: getting derivatives from spline By: jameskuyper on Mon, 13 April 2009 09:54
		Re: getting derivatives from spline By: lbusett@yahoo.it on Sat, 11 April 2009 09:11

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