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  • Filters - summary of repsonses

    Thank you to everyone who responded to my original query:

    I am investigating how several different filtering techniques work.
    While I can find many papers on the application of different filters, I
    have been unable to find any really good sources to explain the
    mechanisms by
    which they operate. I am specifically interested in Butterworth, Splines
    (cubic and quintic) and Woltring filters.

    A summary of responses can be found below:

    Woltring, H.J. (1995). Smoothing and differentiation techniques applied
    3D data.In: Allard, P., Stokes, I.A.F., Blanchi, J.-P.
    (eds.):Three-dimensional analysis of human movement. Champaign, IL:
    Human Kinetics.
    pp. 79-99

    Best regards,
    Nils Betzler
    Dear Eliot,

    >From the Matlab help function I got the following references by looking
    under some of the built-in filtering functions. Hopefully it's of help
    to you.


    [1] Oppenheim, A.V., and R.W. Schafer, Discrete-Time Signal Processing,
    Prentice-Hall, 1989.
    [2] Mitra, S.K., Digital Signal Processing, 2nd ed., McGraw-Hill, 2001,
    Sections 4.4.2 and 8.2.5.
    [3] Gustafsson, F., "Determining the initial states in forward-backward
    filtering," IEEE Transactions on Signal Processing, April 1996, Volume
    44, Issue 4, pp. 988--992, [4] de Boor, C., A Practical Guide to
    Splines, Springer-Verlag, 1978.
    [5] Rabiner, L.R., and B. Gold. Theory and Application of Digital Signal
    Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
    [6] Kaiser, J.F., "Nonrecursive Digital Filter Design Using the - sinh
    Window Function," Proc. 1974 IEEE Symp. Circuits and Systems, (April
    1974), pp. 20-23.
    [7] Selected Papers in Digital Signal Processing II, IEEE Press, New
    York, 1975, pp. 123-126.

    Best regards,

    Vivi M. Thorup
    Ph.D. student
    Hi Eliot,

    Try this book. It is an excellent book in general, but specifically has
    a good description of filtering techniques. This third edition is
    better in this regard than previous editions. Not sure if it is exactly
    what you are looking for, but it is worth a look (especially if you have
    easy access to the book in your university library, or else get it
    through interlibrary loan).


    Hi Eliot,
    Each one of the filters are designed taking into account the spectral
    characteristics of the signals to be treated and the spectral range of
    interest you have. You can filter to remove noise, to separate different
    components of information, to analyze data and so for. Therefore a
    one-email response cannot be complete.
    Butterworth filters for example are basic filters with the frequency
    response being maximally plane (which may be of interest in some cases).
    Splines in general are a way to interpolate data and I have use splines
    in Wavelet filters. I only have heard about Woltring filters and cannot
    say much about that.
    Daniel A. Sierra Bueno
    PhD Student
    Biomedical Engineering
    University of Connecticut
    Dear Eliot

    When I was a PhD student I found Wood,G.A.(1982)Data smoothing and
    differentiation procedures in biomechanics. Exercise and Sports Science
    Reviews. 10,308-362 to be a good starting point to begin to understand
    filtering and smoothing techniques.


    Dr Martin Bailey
    It depends a good deal on what level of information you need. At a
    very basic level, take a look at the Mathworks web site and its section
    on filters. But the best introduction to anything Fourier including
    filters (or windows as they are sometimes called) is Bracewell's book:
    The Fourier Transform and Its Applications. It has pictures that show
    you what is happening and is one of those rare books that is excellent
    for beginners and is still referred to by people spending their lives in
    that field; very clear and correct in almost all details. At a slightly
    more sophisticated level, the best compendium of characteristics of
    filter functions is an old paper by Fredric Harris: "On the Use of
    Windows for Harmonic Analysis with Discrete Fourier Transform"
    Proceedings of the IEEE, Vol 66, No 1, Jan 1978, Pages 51-83. It is a
    great catalogue of filters and their properties. They would include
    good sections on the Butterworth and spline filters.
    As far as "Woltring filters" go, I think those are just higher order
    splines (but could be wrong about that) and are used primarily in Kalman
    filters which are ways of updating and predicting a function (like
    motion). I ran into a pretty good section on Kalman filters on a UNC
    web site:
    which is free and easily accessable.
    There are a host of other filters that use other transforms than the
    Fourier. A common example are wavelet transform filters that allow the
    behavior in time to observed. They allow frequency/time decompositions
    to be done which is useful in motion analysis. Another method of doing
    the same thing is the short time Fourier transform (sometimes called the
    Gabor transform).
    Hope some of that helps.
    Best Regards,

    John B. Weaver, Ph.D.

    As I am unable to send attachments to this posting, please feel free to
    contact me if you would like pdf copies of some articles listed above.


    Eliot Denver

    Postgraduate Scholar
    Cricket Australia / AIS Biomechanics
    Australian Institute of Sport
    Tel +61 2 6214 7892
    Fax +61 2 6214 1593

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