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Jim Martin
09-26-1995, 04:54 AM
Hello all:

After the long debate over quintic and cubic splines, I am reluctant to post
this query, but more feed back is better than less, so here goes.

I am in the process of analyzing a set of data which is collected at even
deltas of position (resulting in unequal delta time). I have found that the
following three techniques yield identical results:

1. Interpolation (to even delta time) and smoothing (smoothing factor =
0.002) with the quintic spline routine of Jennings and Osborne.

2. Interpolation without smoothing with a quintic spline routine, followed
by filtering with a 3rd order recursive Butterworth low pass filter with a
cutoff frequency of 16hz.

3. Interpolation without smoothing with a cubic spline, followed by
filtering with a 3rd order recursive Butterworth low pass filter with a
cutoff frequency of 16hz.

Let me emphasize that these 3 methods yield results that are equivalent
within 0.1% for calculated acceleration throughout the entire data set.

I am reluctant to use the spline smoothing routine because it is somewhat of
a 'black box' approach, and, frankly, I do not understand exactly what
spline smoothing does.

Of the two methods of interpolation and filtering, I can perform the cubic
spline interpolation in Microsoft Excel (using Xlmath), which is very
convenient.

Given that these methods yield equivalent results, I ask you, members of the
biomechanics community, which one is best to use and why? Also, which will
be more readily accepted when submitted for publication?

Thanks in advance for your reply,

Jim Martin, MA, PE
University of Texas at Austin