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I agree in principle with Dr. Hatze's assessment of algorithms for the
determination of optimal cutoff frequencies for filtering and
differentiation of biomechanical data. I believe, however, that it is
important to realize these algorithms cannot always determine good
higher-order derivatives from noisy data. Those who take the time to
truly study and understand the literature in this area are aware of the
underlying assumptions and limitations associated with these methods.
Since I'm not sure everyone interested in this topic falls into that
category, I think it is important to point out some of these issues
here.
The first assumption is that the sampling rate is sufficiently high so
that there is no aliasing of either the desired signal or the noise.
For analog signals, high sampling rates and anti-alias filtering prior
to sampling can be used to insure this. In the case of video-based data
acquisition, this type of filtering is not possible and sample rates are
often limited to 60Hz or less. If the noise or signal frequency is too
high, 2nd derivatives may be terribly inaccurate regardless of filtering
scheme.
The second assumption is that the frequency spectra of the noise and the
frequency spectra of the desired signal do not overlap substantally. If
there is significant overlap then it may not possible to obtain
reasonable acceleration estimates.
The third assumption is that the noise is uncorrelated ("white"). This
is often not the case in biomechanical data - e.g. the "jiggle" which
occurs with a marker affixed to soft tissue on the thigh at footstrike
during running.
I am not trying to imply that the algorithms described by Dr. Hatze are
ineffective or unreliable - used properly, they are extremely useful
tools. My point is that if they are used blindly, the calculated
derivatives may look pretty but be meaningless. I think the only way to
be sure of what you are doing is to try to understand the nature of the
data you are collecting, including the frequencies of motion you are
interested in and the sources and characteristics of noise. Often,
supplementary experiments can be designed (e.g. using accelerometers or
forceplates to estimate frequency content and acceleration magnitude) to
get some answers. Only when you are armed with this information can you
make truly intelligent decisions about data processing. One possible
outcome (that the optimization algorithms do not account for) is that
the chosen data collection scheme is inadequate for determining
higher-order derivatives for the desired motion regardless of
post-processing scheme, in which case more thought needs to go into the
research design.
Thus, I am not convinced that "the wheel has been invented" and that a
simple answer exists. To imply that these algorithms solve all
filtering problems would be misleading, especially to the student
members of the list.
I look forward to feedback from others on this issue.
__________________________________________________ ___________________
Scott Tashman, Ph.D.
Head, Motion Analysis Section Assistant Professor
Bone and Joint Center Department of Orthopaedics
Henry Ford Hospital School of Medicine
2799 W. Grand Blvd. Case Western Reserve University
Detroit, MI 48202
Voice: (313) 876-8680 or 876-7572
FAX: (313) 556-8812 or 876-8064
Internet: tashman@bjc.hfh.edu
__________________________________________________ ___________________
determination of optimal cutoff frequencies for filtering and
differentiation of biomechanical data. I believe, however, that it is
important to realize these algorithms cannot always determine good
higher-order derivatives from noisy data. Those who take the time to
truly study and understand the literature in this area are aware of the
underlying assumptions and limitations associated with these methods.
Since I'm not sure everyone interested in this topic falls into that
category, I think it is important to point out some of these issues
here.
The first assumption is that the sampling rate is sufficiently high so
that there is no aliasing of either the desired signal or the noise.
For analog signals, high sampling rates and anti-alias filtering prior
to sampling can be used to insure this. In the case of video-based data
acquisition, this type of filtering is not possible and sample rates are
often limited to 60Hz or less. If the noise or signal frequency is too
high, 2nd derivatives may be terribly inaccurate regardless of filtering
scheme.
The second assumption is that the frequency spectra of the noise and the
frequency spectra of the desired signal do not overlap substantally. If
there is significant overlap then it may not possible to obtain
reasonable acceleration estimates.
The third assumption is that the noise is uncorrelated ("white"). This
is often not the case in biomechanical data - e.g. the "jiggle" which
occurs with a marker affixed to soft tissue on the thigh at footstrike
during running.
I am not trying to imply that the algorithms described by Dr. Hatze are
ineffective or unreliable - used properly, they are extremely useful
tools. My point is that if they are used blindly, the calculated
derivatives may look pretty but be meaningless. I think the only way to
be sure of what you are doing is to try to understand the nature of the
data you are collecting, including the frequencies of motion you are
interested in and the sources and characteristics of noise. Often,
supplementary experiments can be designed (e.g. using accelerometers or
forceplates to estimate frequency content and acceleration magnitude) to
get some answers. Only when you are armed with this information can you
make truly intelligent decisions about data processing. One possible
outcome (that the optimization algorithms do not account for) is that
the chosen data collection scheme is inadequate for determining
higher-order derivatives for the desired motion regardless of
post-processing scheme, in which case more thought needs to go into the
research design.
Thus, I am not convinced that "the wheel has been invented" and that a
simple answer exists. To imply that these algorithms solve all
filtering problems would be misleading, especially to the student
members of the list.
I look forward to feedback from others on this issue.
__________________________________________________ ___________________
Scott Tashman, Ph.D.
Head, Motion Analysis Section Assistant Professor
Bone and Joint Center Department of Orthopaedics
Henry Ford Hospital School of Medicine
2799 W. Grand Blvd. Case Western Reserve University
Detroit, MI 48202
Voice: (313) 876-8680 or 876-7572
FAX: (313) 556-8812 or 876-8064
Internet: tashman@bjc.hfh.edu
__________________________________________________ ___________________