Scott Tashman, Ph.d.

05-28-1997, 02:48 AM

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

__________________________________________________ ___________________