Re: spline interpolation and

John D'Errico wrote:


Frode wrote:


I have some values sampled at each 0.01 seconds and i have used
a
smoothing cubic spline to interpolate and smooth the contour,
mostly
because i need derivatives.
I seem quite good, but how can i measure the "error"?
Is the word error in this case logic ?
I mean the points plotted gives me a linear approximation to
the
data, so can i say that this is the real data ?
How could i say anything about how good the smoothing really
is?

Hoping for answer.

The first problem is you need to be
specific about what tool you are using.

For example, you use the words smoothing
spline, and interpolation in the same
sentence. But a smoothing spline is not
an interpolant.

An interpolant always reproduces its
data, despite being able to smoothly
interpolate BETWEEN the data points.

So what exactly are you doing? Then
I'll try to answer your questions.

John


I use an apllication called Praat to extract pitch and energy
contours speech samples. The pitch points are extracted every 0.01
seconds. Export the data into matlab and use spline toolbox for
smooting cubic spile. The command was csaps, have tried other methods
to "fit" the data but this seems go give me a great approximation of
the points.

What i meant was that when i reproduce the plot with my original data
with plot-command matlab draw lines betwen the points and my cubic
spline seems to match this with a few exception. I dont think i can
call this graph "the real" graph. Anyway, i have posted 2 pictures to
watch then interpolation. Just look at the upper plots, thats the
data. the circles are my points and the dots are lines connecting
the. The other are the spline.

Would be grateful for some help for how to measure some error or
justify this method due to some measures.
link to plots:

<http://www.stromhaug.no/pics/>
.

Relevant Pages

  • Re: Numerical integration at arbitrary x
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  • Re: Numerical integration at arbitrary x
    ... unknown positions using a high order local interpolation. ... with the grid halved and applied tio the spline in order to get the spline ... smooth the data by a smoothing spline and integrate this one. ...
    (sci.math.num-analysis)
  • Re: Numerical integration at arbitrary x
    ... > unknown positions using a high order local interpolation. ... > with the grid halved and applied tio the spline in order to get the spline ... > smooth the data by a smoothing spline and integrate this one. ... there is an appropriate refinement of this naive technique that is more accurate. ...
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