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Summary of Signal Processing

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  • Summary of Signal Processing

    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
    answering my questions. I wrote:

    "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."

    Raymond P. Young wrote: "You have been thorough about your signal
    processing, having validated your methodologies including examining
    acceleration profiles; therefore, presentation of any technique should be
    acceptable, as your cross-validation tests can be mentioned in one sentence
    or less."

    Kieran Moran wrote: "With regard to the >>journal review process