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To the Biomch-L readership:
Herbert Hatze says that:
> In general, there is agreement that more sophisticated algorithms
> than "guessing" or otherwise "estimating" cut-off frequencies should
> be used for the smoothing and derivative computation of noisy data.
That may not always be true. For instance, one could base the
degree of smoothing on how well the data fit with the laws of mechanics.
For instance, in a jump from the ground after a run-up (in which there
generally is a loss of horizontal velocity during the takeoff phase), one
could look for the best compromise in the degree of smoothing that makes the
horizontal velocity of the c.m. be close to constant (i.e., almost free of
high frequency noise) during the two airborne periods (before and after the
last ground-contact takeoff phase), while not allowing the smoothed
horizontal velocity curve to change value in the neighborhood of (but
outside) the takeoff phase. For instance,
takeoff
phase
* * * * | |
* | |
* |
| * |
| * |
| * |
| * |
| *
| | *
| | * * * * * * *
^
|
This smoothed curve | would not be good, because of oversmoothing.
This curve | would probably be better.
|
\ /
|
takeoff
phase
* * * *| |
* * * |* |
| ** |
| |
| * |
| * |
| * |
| |
| * * | * * *
| | * * * *
And this one | would be too UNDERsmoothed..
|
\ /
|
takeoff
* phase
* | |
* * |* |
* | * |
* * | * |
| * |
| * * |
| | *
| | *
| | *
| * | * *
* *
*
A similar approach could be used with other mechanical parameters,
such as angular momentum about the c.m. (which has to be constant in the
air), or the vertical motion of the c.m. (which has to follow a parabola of
second derivative equal to -9.81 m/s2, which implies a straight vertical
velocity vs time graph with a known downward slope).
The "automatic smoothing" methods generally don't have any built-in
information about the laws of mechanics, and therefore cannot use such
information when they are choosing a value for the smoothing factor. A
human operator CAN make such decisions taking into account the laws of
mechanics. It should be possible to make a computer program that will mimic
the decision process followed by the human operator, and which will take
into account not only the frequency characteristics of the data points
themselves, but also the laws of mechanics. However, it would probably be a
tough program to devise. I have not yet seen an automatic method that I
would trust more than my own visual inspection, although I can see how such
a program might become available at some point in the future.
Also, and inevitably, deciding upon a smoothing factor ultimately
involves a human's choice at one point or another of the process. This
choice could be in the selection of a parameter that is used as input to the
program, or it could be inherent in the program itself. Hatze says that
(according to Yu and also to Orendurff) Winter's method may lead to
oversmoothing, and I have also heard from many people that Woltring's
approach generally UNDERsmooths the data. I have not heard any comments
about the method devised by Hatze, so I am unable to judge how well it works
in practice.
The one thing that seems clear to me is that this topic is not a
dead issue!!
Jesus Dapena
---
Jesus Dapena
Department of Kinesiology
Indiana University
Bloomington, IN 47405, USA
1-812-855-8407
dapena@valeri.hper.indiana.edu
http://www.indiana.edu/~sportbm/home.html
Herbert Hatze says that:
> In general, there is agreement that more sophisticated algorithms
> than "guessing" or otherwise "estimating" cut-off frequencies should
> be used for the smoothing and derivative computation of noisy data.
That may not always be true. For instance, one could base the
degree of smoothing on how well the data fit with the laws of mechanics.
For instance, in a jump from the ground after a run-up (in which there
generally is a loss of horizontal velocity during the takeoff phase), one
could look for the best compromise in the degree of smoothing that makes the
horizontal velocity of the c.m. be close to constant (i.e., almost free of
high frequency noise) during the two airborne periods (before and after the
last ground-contact takeoff phase), while not allowing the smoothed
horizontal velocity curve to change value in the neighborhood of (but
outside) the takeoff phase. For instance,
takeoff
phase
* * * * | |
* | |
* |
| * |
| * |
| * |
| * |
| *
| | *
| | * * * * * * *
^
|
This smoothed curve | would not be good, because of oversmoothing.
This curve | would probably be better.
|
\ /
|
takeoff
phase
* * * *| |
* * * |* |
| ** |
| |
| * |
| * |
| * |
| |
| * * | * * *
| | * * * *
And this one | would be too UNDERsmoothed..
|
\ /
|
takeoff
* phase
* | |
* * |* |
* | * |
* * | * |
| * |
| * * |
| | *
| | *
| | *
| * | * *
* *
*
A similar approach could be used with other mechanical parameters,
such as angular momentum about the c.m. (which has to be constant in the
air), or the vertical motion of the c.m. (which has to follow a parabola of
second derivative equal to -9.81 m/s2, which implies a straight vertical
velocity vs time graph with a known downward slope).
The "automatic smoothing" methods generally don't have any built-in
information about the laws of mechanics, and therefore cannot use such
information when they are choosing a value for the smoothing factor. A
human operator CAN make such decisions taking into account the laws of
mechanics. It should be possible to make a computer program that will mimic
the decision process followed by the human operator, and which will take
into account not only the frequency characteristics of the data points
themselves, but also the laws of mechanics. However, it would probably be a
tough program to devise. I have not yet seen an automatic method that I
would trust more than my own visual inspection, although I can see how such
a program might become available at some point in the future.
Also, and inevitably, deciding upon a smoothing factor ultimately
involves a human's choice at one point or another of the process. This
choice could be in the selection of a parameter that is used as input to the
program, or it could be inherent in the program itself. Hatze says that
(according to Yu and also to Orendurff) Winter's method may lead to
oversmoothing, and I have also heard from many people that Woltring's
approach generally UNDERsmooths the data. I have not heard any comments
about the method devised by Hatze, so I am unable to judge how well it works
in practice.
The one thing that seems clear to me is that this topic is not a
dead issue!!
Jesus Dapena
---
Jesus Dapena
Department of Kinesiology
Indiana University
Bloomington, IN 47405, USA
1-812-855-8407
dapena@valeri.hper.indiana.edu
http://www.indiana.edu/~sportbm/home.html