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Dear Biomch-l subscribers
I was glad to see the message of Prof Herbert Hatze concerning biomechanical
data smoothing and differentiation. I would like to make some
comments on his message; there are some points in which I agree but
there are some others in which I personally don't.
To start with, I agree that Winter's residual analysis underestimates
the optimal cut-off frequency resulting in oversmoothing of displacement
data (Giakas and Baltzopoulos, 1997a).
I also agree with the comment that optimally filtered derivatives can,
in general, NOT be obtained by simply differentiating the smoothed
signal. A different differentiation strategy is required and this is
well explained in Giakas and Baltzopoulos (1997b), although further
investigation is required.
Information concerning the higher derivatives is also required for
optimal results. The optimal filtering - differentiation sequence,
however, is NOT by first differentiating and then filtering the data
as used in the algorithm presented by Hatze (1979, 1981, 1990).
As Prof Hatze said, the regularisation of Fourier Series results in an
estimation of a cut-off frequency ("optimal" filtering window). This
cut-off is considered as optimal, and the overall filtering method as
appropriate for biomechanical purposes.
At this stage however, I might dissapoint Prof. Hatze.
Our study (Giakas and Baltzopoulos, 1997a) compared six automatic
filtering techniques (one of those was optimal regularisation of Fourier
Series, (Anderssen and Bloomfield, 1974) - which is quite similar to
Hatzes' (1981) algorithm), using walking data (approximately 1440
signals made by different reference and noise time/frequency domain
characteristics).
The results showed that among the investigated techniques, the
performance of RFS was poor. Just for the history, generalised cross
validated splines was better than RFS, but not the overall best of
the study.
There was not one filtering technique that would perform better than
all the others for all signals, and therefore we came back to the
same conclusion that there is not an optimal filtering solution for
all different types of signals. Therefore before filtering the data,
it is always good to know some of their characteristics, but also be
aware of the assumptions and limitations of each automatic filtering
technique. The "black-box" approach is certainly not advised,
otherwise...
As a last comment to finish this message, I don't thing that we, or
the students, are reinventing the wheel, since there are a lot of
problems in this area and further investigation is required. If
somebody asks me to suggest an automatic filtering technique
appropriate for gait analysis, then I would obviously suggest the top
ones that we found from our study, but I would not be confident that
they would be the best if I don't know the type of movement, the type
of signals, the sampling frequency, the precision of the
equipment used, the quality of calibration,... etc. and see the
signal characteristics in time and frequency domain.
Thank you for your attention, and I look forward to see more comments
on this "hot" topic.
Giannis
PS The abstacts of our papers can be found in ISB WWW /biomechanical
data sources section.
References
Anderssen, R. S. and Bloomfield, P. (1974). Numerical differentiation procedures for non-exact
data. Numer. Math. 22, 157-182.
Giakas, G. and Baltzopoulos, V. (1997a). A comparison of automatic
filtering techniques applied to biomechanical walking data.
J. Biomechanics In Press.
Giakas, G. and Baltzopoulos, V. (1997b). Optimal digital filtering
requires a different cut-off frequency strategy for the determination
of the higher derivatives. J. Biomechanics In Press.
Hatze, H. (1979). An algorithm for computing higher order derivatives
of noisy experimental data sequences (Rep No TWISK 123). Nasionale
Navorsingsinstituut vir Wiskundige Wetenskappe, Pretoria.
Hatze, H. (1981). The use of optimally regularized Fourier series
for estimating higher-order derivatives of noisy biomechanical data.
J. Biomechanics 14, 13-18.
Hatze, H. (1990). Data conditioning and differentiation techniques.
In Biomechanics of human movement: applications in rehabilitation,
sports and ergonomics p. 237-248 (Edited by N. Berme & A. Cappozzo),
Bertec Corporation, Worthinghton, OH.
--
Giannis Giakas
Lecturer in Biomechanics
Division of SHE
Staffordshire University
Stoke-on-Trent ST4 2DF
Tel : +44 1782 294292
Fax : +44 1782 747167
Email: g.giakas@staffs.ac.uk
I was glad to see the message of Prof Herbert Hatze concerning biomechanical
data smoothing and differentiation. I would like to make some
comments on his message; there are some points in which I agree but
there are some others in which I personally don't.
To start with, I agree that Winter's residual analysis underestimates
the optimal cut-off frequency resulting in oversmoothing of displacement
data (Giakas and Baltzopoulos, 1997a).
I also agree with the comment that optimally filtered derivatives can,
in general, NOT be obtained by simply differentiating the smoothed
signal. A different differentiation strategy is required and this is
well explained in Giakas and Baltzopoulos (1997b), although further
investigation is required.
Information concerning the higher derivatives is also required for
optimal results. The optimal filtering - differentiation sequence,
however, is NOT by first differentiating and then filtering the data
as used in the algorithm presented by Hatze (1979, 1981, 1990).
As Prof Hatze said, the regularisation of Fourier Series results in an
estimation of a cut-off frequency ("optimal" filtering window). This
cut-off is considered as optimal, and the overall filtering method as
appropriate for biomechanical purposes.
At this stage however, I might dissapoint Prof. Hatze.
Our study (Giakas and Baltzopoulos, 1997a) compared six automatic
filtering techniques (one of those was optimal regularisation of Fourier
Series, (Anderssen and Bloomfield, 1974) - which is quite similar to
Hatzes' (1981) algorithm), using walking data (approximately 1440
signals made by different reference and noise time/frequency domain
characteristics).
The results showed that among the investigated techniques, the
performance of RFS was poor. Just for the history, generalised cross
validated splines was better than RFS, but not the overall best of
the study.
There was not one filtering technique that would perform better than
all the others for all signals, and therefore we came back to the
same conclusion that there is not an optimal filtering solution for
all different types of signals. Therefore before filtering the data,
it is always good to know some of their characteristics, but also be
aware of the assumptions and limitations of each automatic filtering
technique. The "black-box" approach is certainly not advised,
otherwise...
As a last comment to finish this message, I don't thing that we, or
the students, are reinventing the wheel, since there are a lot of
problems in this area and further investigation is required. If
somebody asks me to suggest an automatic filtering technique
appropriate for gait analysis, then I would obviously suggest the top
ones that we found from our study, but I would not be confident that
they would be the best if I don't know the type of movement, the type
of signals, the sampling frequency, the precision of the
equipment used, the quality of calibration,... etc. and see the
signal characteristics in time and frequency domain.
Thank you for your attention, and I look forward to see more comments
on this "hot" topic.
Giannis
PS The abstacts of our papers can be found in ISB WWW /biomechanical
data sources section.
References
Anderssen, R. S. and Bloomfield, P. (1974). Numerical differentiation procedures for non-exact
data. Numer. Math. 22, 157-182.
Giakas, G. and Baltzopoulos, V. (1997a). A comparison of automatic
filtering techniques applied to biomechanical walking data.
J. Biomechanics In Press.
Giakas, G. and Baltzopoulos, V. (1997b). Optimal digital filtering
requires a different cut-off frequency strategy for the determination
of the higher derivatives. J. Biomechanics In Press.
Hatze, H. (1979). An algorithm for computing higher order derivatives
of noisy experimental data sequences (Rep No TWISK 123). Nasionale
Navorsingsinstituut vir Wiskundige Wetenskappe, Pretoria.
Hatze, H. (1981). The use of optimally regularized Fourier series
for estimating higher-order derivatives of noisy biomechanical data.
J. Biomechanics 14, 13-18.
Hatze, H. (1990). Data conditioning and differentiation techniques.
In Biomechanics of human movement: applications in rehabilitation,
sports and ergonomics p. 237-248 (Edited by N. Berme & A. Cappozzo),
Bertec Corporation, Worthinghton, OH.
--
Giannis Giakas
Lecturer in Biomechanics
Division of SHE
Staffordshire University
Stoke-on-Trent ST4 2DF
Tel : +44 1782 294292
Fax : +44 1782 747167
Email: g.giakas@staffs.ac.uk