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Artifacts and splines

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  • Artifacts and splines

    Dear subscribers,

    Reading mail from BIOMCH-L regarding splines, I learned that some of
    you observed splines sometimes produce artifacts in the smoothed data.
    The artifacts caused by quintic splines have been reported to be more
    marked than those generated by cubic spline.

    Is there anyone who can give exact answers to the following
    important questions?

    1) Are the artifacts present (a) only in the middle of each cubic or
    quintic polinomial, or (b) also in the extremes (corresponding to the instants
    when the raw data were measured)?
    In case (a) only interpolated data would be affected, while in case
    (b) also non-interpolated data might contain unwanted extra-noise.
    Van der Bogert and Glossop wrote that they noticed artifacts in
    interpolated data (case a). I would like to know for sure if artifacts
    can be excluded at the extremes of each polinomial (case b).

    2) Does this uncertainty in the results have a clean mathematical
    explanation? It was not clear whether the artifacts were just observed
    by some researchers, USING SOME PARTICULAR SPLINE ROUTINES, or they are
    expected, embedded in the logic of the equations themselves, and cannot be
    avoided, whatever routine you are using.

    3) Are the artifacts mathematical singularities, that occur only in
    some precise cases, or they occur unpredictably?

    I would appreciate answers by somebody who studied the mathematics of
    splines. I believe that many people (me included of course) use splines without
    knowing the details of the algorithms, and I believe an explanation given
    through BIOMCH-L would be an important contribution to the world community of
    biomechanists (I apologize if this is not true, and only some fiends of mine
    are as ignorant as I am).

    With regards,

    Paolo de Leva
    P.S. By the way, I know Jesus Dapena, his care for details, and his capability
    to discover bugs and spot bad data. Since he never noticed the artifacts in his
    long career I find it hard to believe that these artifacts are a real and
    present risk. Anyway, I will be glad to accept the evidence if someone can
    convince me about the contrary (just in case the contrary is actually true,
    of course).

    __________ _________ ___________~___ ________ _________________~___
    / ~ ~ ~ ~ \
    /______________~______~__________ _______~_____~______________~_____~_____\
    | Paolo de Leva ~ \ Tel.+ FAX: (39-6) 575.40.81 |
    | Istituto Superiore di Educazione Fisica > other FAX: (39-6) 361.30.65 |
    | Biomechanics Lab / |
    | Via di Villa Pepoli, 4 < INTERNET e-mail address: |
    | 00153 ROME - ITALY \ deLEVA@RISCcics.Ing.UniRoma1.IT |
    |_____________________~________~__________________ __________________ _____|
    challenging entropy :-)