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Jim Martin
10-08-1995, 12:25 AM
Thanks to all who responded to my posting, especially Dr. Ton van den
Bogert, Dr. Jesus Dapena, and Dr. Steve Kautz who spent a lot of time

"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 16 Hz.

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 16 Hz.

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?"

I should add that my raw data is delta time for a known delta theta, so I
sart with velocity as my raw data (time-velocity).

I received several replies of support for the approaches I described.

Dr. Jesus Dapena wrote: "Given the results that you are getting, I see no
problem in using either of the three methods for the particular application
that you need. (I don't know if the three options will be equivalent in
OTHER situations.)"
Dr. Dapena also provided me with a very thorough explanation of how the
Jennings and Osborne spline smoothing routine works and possible problems
that I might encounter with it. Specifically, "...Jennings' smoothing factor
is the sum of the squares of the differences between the raw data and the
smoothed data."

Dr. Steve Kautz wrote: "As long as the answer is essentially the same in
your application, you are justified in using the one that makes your
analysis most efficient."
Dr. Kautz also suggested: "The best way to address this problem is to show a
plot of the raw data with the smoothed/filtered data superimposed. Maybe do
a residual analysis and show that the residuals are random. Then a reviewer
would be quibbling if they still refused to accept your technique."

Dr. Richard N. Hinrichs wrote: "Just go ahead and use the quintic spline for
both interpolation and smoothing. Why go through two steps? You should not
receive any objections from reviewers for using the quintic spline."