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Eliot Denver
10-23-2006, 09:25 AM
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
to
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.

References

[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).

http://search.barnesandnoble.com/booksearch/isbnInquiry.asp?z=y&EAN=9780
471449898&itm=1


Regards,

Brian
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.
Sincerely,
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.

Regards

Dr Martin Bailey
Eliot,
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:
http://www.cs.unc.edu/~tracker/media/pdf/SIGGRAPH2001_CoursePack_08.pdf
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.

Regards,

Eliot Denver

Postgraduate Scholar
Cricket Australia / AIS Biomechanics
Australian Institute of Sport
Tel +61 2 6214 7892
Fax +61 2 6214 1593
Email eliot.denver@ausport.gov.au


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