Thankyou very much to all of you who responded to my request for information and

opinions on selecting the optimal cutoff frequency for a Butterworth filter

applied to

displacement - time data collected from a rotary encoder. Please find

following my

original posting and the replies that I received.

Regards

Robert Newton

MY POSTING

I have been analysing the signal from a rotary encoder which provides

displacement time data in an attempt to determine the optimal cut-off

frequency for filtering the data prior to differentiation to provide

velocity and acceleration data. I have been smoothing the data using

a Butterworth 4th Order digital filter with cutoff frequencies ranging from

1 to 60Hz and subsequently calculating the residual as the mean square

difference between the filtered and raw data. Having plotted the residual

against cutoff frequency I have been attempting to determine the optimal

cutoff frequency by projecting the linear part of the resulting curve to

the vertical axis and then back to the curve to determine the cutoff. The

process is outlined on pages 41-43 of David Winter's book

"Biomechanics and Motor Control of Human Movement, 2nd Edition".

My problem is that the plot at the higher cutoff frequencies is not linear

but curvelinear and I an unable to determine over what range of cutoff

frequencies should I project my line from. The calculated optimal cutoff

frequency is affected to a great extent by what range I define as the

linear part of the curve.

Can anyone provide advice on how I might determine my optimal

cutoff frequency? Is there a source of a more detailed explanation of the

method for determining optimal cutoff frequency?

REPLIES

================================================== ========

Date: Mon, 21 Nov 1994 15:38:51 -0600 (CST)

X-Ph: V4.1@genesis

From: YUB@rcf.mayo.edu

To: run1@psu.edu

Subject: RE: Optimal cutoff frequency for data smoothing

Hi, Robert,

When I was at Kansas State Univeristy, I did a study on determination of the

optimum cutoff frequency for the digital filter data smoothing procedure. I

used a set of theoretical data as standard data, and added random errors into

this set of standard data to get different sets of "raw data". The raw data

was smoothed using the digital filter you used at different cutoff frequencies.

I calculated the accelerations from the smoothed raw data. When the calculated

acceleration data had the maximum similarity with the theoretical acceleration

data, the cutoff frequency was considered as the optimum. It was found that

the optimum cutoff frequency and the sampling frequency were significantly

correlated. The optimum cutoff frequency can be estimated using

Fc = (1.4845 + 0.1523 Fs^1/2)^2

This equation explained over 75% of the total variation in the optimum cutoff

frequency. This equation has been used in the last five years for different 2d

and 3d coordinate data in different human body motions, and the results are

satisfactory. The explanation for this relationship is that the higher the

sampling frequency, the high the frequency of the random error (the further

the random error components will go to the high frequency end of the frequency

spectrum, see Dr. Winter's book, Biomechanics of human movement.). You may try

this equation if you think it makes sense or its smoothing results make sense.

I also have another equation for determination of optimum cutoff frequency,

which requires FFT and freqeuncy analysis. It explained over 85% of the total

variation of the optimum cutoff frequency. However, I found that sometimes this

equation works pretty well, sometimes doesn't. If you are interested in, I can

give you all the details.

Several years ago, I tried to get the study published in Journal of

Biomechanics as a technical note. One of the reviewer attacked me saying that

this study had no contribution to the biomechanics. But the how to determine

the optimum cutoff frequency has been frequently asked by many researchers in

biomechanics in the last several years. It may be the time for me to

re-consider publishing this study.

Bing Yu, Ph.D.

Orthopedic Biomechanics Laboratory

Mayo Clinic

Rochester, MN 55905

================================================== =======

Date: Mon, 21 Nov 1994 16:19:15 -0600

X-Ph: V4.1@genesis

From: Duane Knudson

Subject: RE>Optimal cutoff frequency for data smoothing

To: Robert Newton

Greetings Robert!

I bet you get a large number of responses to this post since data smoothing

has been a persistent problem in our field. I have RMS residuals for many

kinds of kinematic data and get curves very similar to Winter's 2.25 on page

43. The curves tend to bottom out at the measurement error for the situation.

I do not suspect the mean square error would be any different.

The problem is that even the "automated" smoothing programs essentially are

still arbitrary selections (note that Winter p. 42 says " If we decide both (

signal distortion and noise passed) should be equal . . ." The other

arbitrary "automated" method is the Jackson (1979) method that takes the

second derivative of the linear interpolation of the residuals. It may be a

chicken/egg situation where we cannot objectively separate the signal and

noise of our kinematic data. Even fourier analysis, ultimately must be based

on some guess (95% signal power?) as a good compromise of signal distortion

and nois attenuation.

We need more accelerometer studies and a common standard of what is acceptable

signal to noise ratio, or what are appropriate frequencies for specific kinds

of biomechanical data. Good luck in your quest.

Jackson, K.M. (1979) Fitting of mathematical functions to biomechanical data.

IEEE Trans Biomed Eng. 26:122-124.

================================================== ====

Robert:

Just out of curiuosity, what is your sampling rate? Since you are smoothing

up to 60 Hz, it almost sounds as if you are violating the Nyquist limit of

the Butterworth digital filter (see J. Walton's dissertation). Once beyond

(0.25 * SAMPLING_RATE), the Butterworth digital filter behaves strangely.

Could this be the problem? If, for example, you are collecting at 100 Hz,

try using your algorithm in the cutoff range of 1-25 and see if that

eliminates the strange sections of the residual curve. Good luck -- let me

know what happens.

Peter Vint

Arizona State University

Exercise and Sport Research Institute

VINT@ESPE1.LA.ASU.EDU

(Note sampling frequency was 500 Hz - Robert Newton)

================================================== ==

Date: Tue, 22 Nov 94 11:24:08 EST

X-Ph: V4.1@genesis

From: Tim=Wrigley%PhysEd_Rec%VUT@gnu.vut.edu.au

Subject: optimal filtering

To: run1@psu.edu

Cc:

Hi Rob

You might try the Jackson 'knee' method:

Jackson, KM (1979) Fitting of mathematical functions to biomechanical data.

IEEE Trans. Biomed. Eng., vol ?:122-124.

I haven't got Winter in front of me, and I can't remember the specifics of

the method he suggests. It may even be the Jackson method, in which case I

haven't helped you much !

The Jackson method is now used by the Peak system for optimal filtering by

Butterworth, cubic spline, or fourier series. It seems to work well for

kinematic data, but I haven't tried it for anything more complex.

Good luck !

Cheers

Tim

================================================== ===

X-Ph: V4.1@genesis

To: run1@psu.edu

From: "Alan Walmsley"

Organization: School of Physical Education, Otago

Date: Tue, 22 Nov 1994 15:03:17 GMT+1200

Subject: Re: Optimal cutoff frequency for data smoothing

Priority: normal

Dear Robert,

Have you considered spectral analysis to obtain the major frequency

components, and then choosing a cut-off frequency at least an octave

above the major peak?

Alan Walmsley

School of Physical Education

Division of Sciences

University of Otago

Dunedin, New Zealand.

Ph (03) 4799122, Fax (03) 4798309

=================================================

X-Ph: V4.1@genesis

To: run1@psu.edu

From: Rob Neal

Date: Tue, 22 Nov 1994 12:41:11 EST5EDT

Subject: Re: Optimal cutoff frequency for data smoothing

Priority: normal

I don't have the references but the problem seems very similar to the

one exercise physiologists have for determining ventilatory threshold

or anaerobic threshold. There are a few papers detailing various

methods to solve this problem. I could try to find them from the guys

at the QAS if you would like.

Cheers,

Rob

Robert Neal, PhD

Department of Human Movement Studies

The University of Queensland

QLD, AUSTRALIA

ph 61 7 365 6240

FAX 61 7 365 6877

EMAIL NEAL@HMS01.HMS.UQ.OZ.AU

================================================

Date: Tue, 22 Nov 1994 09:33:26 -0500 (EST)

X-Ph: V4.1@genesis

From: stuart mcgill

Subject: Re: Optimal cutoff frequency for data smoothing

To: Robert Newton

Hello Robert,

"Residual analysis" as described in Winter assumes that the noise

component is white- yours appears not to be. Perhaps you should attempt

another method- you didn't describe the signal that must be smoothed-

this would help in choosing another way to smooth. Good luck.

Stu McGill

================================================

Date: Tue, 22 Nov 1994 12:45:32 MET-DST

X-Ph: V4.1@genesis

From: "Giovanni LEGNANI. Uni. of Brescia, Italy EC"

Subject: Re: Optimal cutoff frequency for data smoothing

To: run1@psu.edu

X-Vms-To: IN%"run1@PSU.EDU"

-----------------------

The frequency should be proportional to the frequency of the incoming pulses

coming from the encoders. (you are forced to choose the maximum speed).

then you have to choose a frequency that is lower than the half of the

incoming signal of angle to avoid fenomena similar to aliasing.

so if you have an encoder haning 1000 steps, you will have 4000 samples

per turn.

if your encoder rotates ad a speed of K turns per second you have a data

frequency of 4000 Hz. I suggest you to filter chosing a low-pass filter

having a bandwith lower than 2000 Hz.

Better a little lower.

take in mind that an encoder give an approximate value for the angle.

the absolute error is 1 step. when the encoder rotates you have a noise

having an amplitude of 1 step and a frequency proportional to the

encoder speed and to the number of the encoder steps.

bye

giovanni legnani

===============================================

X-Ph: V4.1@genesis

From: "Tom Lundin"

Date: Tue, 22 Nov 94 11:04:32 EDT

Reply-To:

X-Popmail-Charset: English

To: run1@psu.edu

Subject: cutoff frequencies

Robert,

I have recently encountered a similar problem with filtering motion data.

The best algorithm I could come up with to select a cutoff was to

differentiate the RMS error vs. cutoff frequency twice and search for where

the ensuing curve approximated zero (point Z). I found the slope of the

line described by Winter from the first derivative of the RMS curve at Z.

Then using the equation of that line I found the cutoff frequency as I

presume you already know how to do. If you have any questions or comments

please feel free to write back. I hope this helps and I'll be interested

to see the other responses you receive.

Regards,

Tom Lundin

The Cleveland Clinic Foundation

================================================== ==

X-Ph: V4.1@genesis

From: Paul Guy

Subject: Re: Optimal cutoff frequency for data smoothing

To: run1@psu.edu

Date: Tue, 22 Nov 1994 12:30:55 -0500 (EST)

Content-Length: 4111

Having worked with Dave Winter for many years in his lab, I'll give

you an answer you might not want to hear.

In short, there is no decent mathematical method that I've seen based

on conventional or residual analysis that covers all the situations. If

you are interested in say just the displacements, then a residual

analysis of them will probably do, if you wanted to see what gave the

best results in a power or kinetics situation, then you'd need to do

residuals based on those variables.

The best way to deal with it, is to have some previous knowledge of

the system you are measuring, what its dynamic characteristics are, and

what the behaviour is of the data once it arrives at your computer. Such

things as whether you used interlaced video would be very important

(large 30 hz noise components), or where the resonant frequencies were

on your force plates, transducers etc.

For filtering data from the human body, we will filter different

segments at different frequencies, for example the trunk markers at 1-3

Hz, the foot at 8 to 15 Hz depending on the activity.

Where the accelerations become very important, we find that it's often

worthwhile to raise the sampling frequency, especially if you are doing

stuff like FFT's (and you need long records too). The ratio of cutoff

frequency to sampling frequency will affect whether you are really

getting an analog equivalent. Filtering at 1/4 the sampling frequency

will not give you the characteristics that you might expect.

Another issue is filter TYPE.... are you using Butterworth, Bessel,

IIR,FIR, 2-way pass etc. ? All these become an issue depending on what

you're looking at, in what domain, and how your applications are going

to react to the various 'corruptions'. For example, we use a so-called

4th order 2-way Butterworth (it's run through two 2nd order

Butterworths, the second is filtered backwards in time, to reduce delay

artifacts). Using this filter with force plates causes a force to appear

on the plate before the foot contacts it. That's clearly silly data.

Similiarly, the horizontal impulse the foot gives at heel contact can

really mess up the determination of the body kinetics.....filtering it

can spread what occurs in 10-50ms over a much longer time, rendering

your analysis useless near heel contact.

Don't buy all that theory stuff, sometimes a look at the big picture

will help more.

-Paul

-----------------------------------------------------------------------------

Paul J Guy work phone:519-885-1211 ext 6371

paul@gaitlab1.uwaterloo.ca home/FAX/:519-576-3090

pguy@healthy.uwaterloo.ca 64 Mt.Hope St.,Kitchener,Ontario,Canada

================================================== =

Date: Tue, 22 Nov 1994 11:45:26 -0600 (CST)

X-Ph: V4.1@genesis

From: "Christine Q. Wu"

To: Robert Newton

Subject: Re: Optimal cutoff frequency for data smoothing

Dear Robert: I have the similar problem. Would you please let me know if

you get any solution. Besides, is the range of motion effects the smooth

procedure? If the range of motion is low, may be comparable with the

magnitude of the noise, what will happen?

Good luck!

Christine

================================================== =

Date: 22 Nov 94 16:39:49 EST

X-Ph: V4.1@genesis

From: "Peak Performance Tech."

To: Robert Newton

Subject: Re: Optimal cutoff frequency for data smoothing

Robert-

If you haven't already, you may want to check out the "Jackson Knee

Method". It plots the 2nd derivative of the percent average residual

curve vs. the cutoff frequency. When three points on that curve fall

below a defined prescribed limit, the smallest frequency of the curve

becomes the optimal.

Jackson, K.M. Fitting of mathematical functions to biomechanical data.

IEEE Transactions on Biomedical Engineering, 1979, pp. 122-124.

*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

George Miller

Peak Performance Technologies

Englewood, CO

76244.3047@CompuServe.com

*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

==================================================

Date: Tue, 22 Nov 1994 21:58:37 -0600 (CST)

X-Ph: V4.1@genesis

From: "M. Pizzimenti"

Subject: Re: Optimal cutoff frequency for data smoothing

To: Robert Newton

Robert,

Try Jackson's algorithm where the residuals are differentiated.

Jackson, K.M. Fitting of mathematical functions to biomechanical data.

IEEE Transactions of Biomedical Engineering BME26(2), 122-124, 1979

Hope this helps

Marc Pizzimenti

University of Iowa

Department of Exercise Science

====================== END OF REPLIES =================

--

Robert Newton Phone Int+ 1 814

865 7107

Center for Sports Medicine Fax Int+ 1 814 865 7077

The Pennsylvania State University Email RUN1@PSU.EDU

117 Ann Building

University Park, PA 16802

United States of America

opinions on selecting the optimal cutoff frequency for a Butterworth filter

applied to

displacement - time data collected from a rotary encoder. Please find

following my

original posting and the replies that I received.

Regards

Robert Newton

MY POSTING

I have been analysing the signal from a rotary encoder which provides

displacement time data in an attempt to determine the optimal cut-off

frequency for filtering the data prior to differentiation to provide

velocity and acceleration data. I have been smoothing the data using

a Butterworth 4th Order digital filter with cutoff frequencies ranging from

1 to 60Hz and subsequently calculating the residual as the mean square

difference between the filtered and raw data. Having plotted the residual

against cutoff frequency I have been attempting to determine the optimal

cutoff frequency by projecting the linear part of the resulting curve to

the vertical axis and then back to the curve to determine the cutoff. The

process is outlined on pages 41-43 of David Winter's book

"Biomechanics and Motor Control of Human Movement, 2nd Edition".

My problem is that the plot at the higher cutoff frequencies is not linear

but curvelinear and I an unable to determine over what range of cutoff

frequencies should I project my line from. The calculated optimal cutoff

frequency is affected to a great extent by what range I define as the

linear part of the curve.

Can anyone provide advice on how I might determine my optimal

cutoff frequency? Is there a source of a more detailed explanation of the

method for determining optimal cutoff frequency?

REPLIES

================================================== ========

Date: Mon, 21 Nov 1994 15:38:51 -0600 (CST)

X-Ph: V4.1@genesis

From: YUB@rcf.mayo.edu

To: run1@psu.edu

Subject: RE: Optimal cutoff frequency for data smoothing

Hi, Robert,

When I was at Kansas State Univeristy, I did a study on determination of the

optimum cutoff frequency for the digital filter data smoothing procedure. I

used a set of theoretical data as standard data, and added random errors into

this set of standard data to get different sets of "raw data". The raw data

was smoothed using the digital filter you used at different cutoff frequencies.

I calculated the accelerations from the smoothed raw data. When the calculated

acceleration data had the maximum similarity with the theoretical acceleration

data, the cutoff frequency was considered as the optimum. It was found that

the optimum cutoff frequency and the sampling frequency were significantly

correlated. The optimum cutoff frequency can be estimated using

Fc = (1.4845 + 0.1523 Fs^1/2)^2

This equation explained over 75% of the total variation in the optimum cutoff

frequency. This equation has been used in the last five years for different 2d

and 3d coordinate data in different human body motions, and the results are

satisfactory. The explanation for this relationship is that the higher the

sampling frequency, the high the frequency of the random error (the further

the random error components will go to the high frequency end of the frequency

spectrum, see Dr. Winter's book, Biomechanics of human movement.). You may try

this equation if you think it makes sense or its smoothing results make sense.

I also have another equation for determination of optimum cutoff frequency,

which requires FFT and freqeuncy analysis. It explained over 85% of the total

variation of the optimum cutoff frequency. However, I found that sometimes this

equation works pretty well, sometimes doesn't. If you are interested in, I can

give you all the details.

Several years ago, I tried to get the study published in Journal of

Biomechanics as a technical note. One of the reviewer attacked me saying that

this study had no contribution to the biomechanics. But the how to determine

the optimum cutoff frequency has been frequently asked by many researchers in

biomechanics in the last several years. It may be the time for me to

re-consider publishing this study.

Bing Yu, Ph.D.

Orthopedic Biomechanics Laboratory

Mayo Clinic

Rochester, MN 55905

================================================== =======

Date: Mon, 21 Nov 1994 16:19:15 -0600

X-Ph: V4.1@genesis

From: Duane Knudson

Subject: RE>Optimal cutoff frequency for data smoothing

To: Robert Newton

Greetings Robert!

I bet you get a large number of responses to this post since data smoothing

has been a persistent problem in our field. I have RMS residuals for many

kinds of kinematic data and get curves very similar to Winter's 2.25 on page

43. The curves tend to bottom out at the measurement error for the situation.

I do not suspect the mean square error would be any different.

The problem is that even the "automated" smoothing programs essentially are

still arbitrary selections (note that Winter p. 42 says " If we decide both (

signal distortion and noise passed) should be equal . . ." The other

arbitrary "automated" method is the Jackson (1979) method that takes the

second derivative of the linear interpolation of the residuals. It may be a

chicken/egg situation where we cannot objectively separate the signal and

noise of our kinematic data. Even fourier analysis, ultimately must be based

on some guess (95% signal power?) as a good compromise of signal distortion

and nois attenuation.

We need more accelerometer studies and a common standard of what is acceptable

signal to noise ratio, or what are appropriate frequencies for specific kinds

of biomechanical data. Good luck in your quest.

Jackson, K.M. (1979) Fitting of mathematical functions to biomechanical data.

IEEE Trans Biomed Eng. 26:122-124.

================================================== ====

Robert:

Just out of curiuosity, what is your sampling rate? Since you are smoothing

up to 60 Hz, it almost sounds as if you are violating the Nyquist limit of

the Butterworth digital filter (see J. Walton's dissertation). Once beyond

(0.25 * SAMPLING_RATE), the Butterworth digital filter behaves strangely.

Could this be the problem? If, for example, you are collecting at 100 Hz,

try using your algorithm in the cutoff range of 1-25 and see if that

eliminates the strange sections of the residual curve. Good luck -- let me

know what happens.

Peter Vint

Arizona State University

Exercise and Sport Research Institute

VINT@ESPE1.LA.ASU.EDU

(Note sampling frequency was 500 Hz - Robert Newton)

================================================== ==

Date: Tue, 22 Nov 94 11:24:08 EST

X-Ph: V4.1@genesis

From: Tim=Wrigley%PhysEd_Rec%VUT@gnu.vut.edu.au

Subject: optimal filtering

To: run1@psu.edu

Cc:

Hi Rob

You might try the Jackson 'knee' method:

Jackson, KM (1979) Fitting of mathematical functions to biomechanical data.

IEEE Trans. Biomed. Eng., vol ?:122-124.

I haven't got Winter in front of me, and I can't remember the specifics of

the method he suggests. It may even be the Jackson method, in which case I

haven't helped you much !

The Jackson method is now used by the Peak system for optimal filtering by

Butterworth, cubic spline, or fourier series. It seems to work well for

kinematic data, but I haven't tried it for anything more complex.

Good luck !

Cheers

Tim

================================================== ===

X-Ph: V4.1@genesis

To: run1@psu.edu

From: "Alan Walmsley"

Organization: School of Physical Education, Otago

Date: Tue, 22 Nov 1994 15:03:17 GMT+1200

Subject: Re: Optimal cutoff frequency for data smoothing

Priority: normal

Dear Robert,

Have you considered spectral analysis to obtain the major frequency

components, and then choosing a cut-off frequency at least an octave

above the major peak?

Alan Walmsley

School of Physical Education

Division of Sciences

University of Otago

Dunedin, New Zealand.

Ph (03) 4799122, Fax (03) 4798309

=================================================

X-Ph: V4.1@genesis

To: run1@psu.edu

From: Rob Neal

Date: Tue, 22 Nov 1994 12:41:11 EST5EDT

Subject: Re: Optimal cutoff frequency for data smoothing

Priority: normal

I don't have the references but the problem seems very similar to the

one exercise physiologists have for determining ventilatory threshold

or anaerobic threshold. There are a few papers detailing various

methods to solve this problem. I could try to find them from the guys

at the QAS if you would like.

Cheers,

Rob

Robert Neal, PhD

Department of Human Movement Studies

The University of Queensland

QLD, AUSTRALIA

ph 61 7 365 6240

FAX 61 7 365 6877

EMAIL NEAL@HMS01.HMS.UQ.OZ.AU

================================================

Date: Tue, 22 Nov 1994 09:33:26 -0500 (EST)

X-Ph: V4.1@genesis

From: stuart mcgill

Subject: Re: Optimal cutoff frequency for data smoothing

To: Robert Newton

Hello Robert,

"Residual analysis" as described in Winter assumes that the noise

component is white- yours appears not to be. Perhaps you should attempt

another method- you didn't describe the signal that must be smoothed-

this would help in choosing another way to smooth. Good luck.

Stu McGill

================================================

Date: Tue, 22 Nov 1994 12:45:32 MET-DST

X-Ph: V4.1@genesis

From: "Giovanni LEGNANI. Uni. of Brescia, Italy EC"

Subject: Re: Optimal cutoff frequency for data smoothing

To: run1@psu.edu

X-Vms-To: IN%"run1@PSU.EDU"

-----------------------

The frequency should be proportional to the frequency of the incoming pulses

coming from the encoders. (you are forced to choose the maximum speed).

then you have to choose a frequency that is lower than the half of the

incoming signal of angle to avoid fenomena similar to aliasing.

so if you have an encoder haning 1000 steps, you will have 4000 samples

per turn.

if your encoder rotates ad a speed of K turns per second you have a data

frequency of 4000 Hz. I suggest you to filter chosing a low-pass filter

having a bandwith lower than 2000 Hz.

Better a little lower.

take in mind that an encoder give an approximate value for the angle.

the absolute error is 1 step. when the encoder rotates you have a noise

having an amplitude of 1 step and a frequency proportional to the

encoder speed and to the number of the encoder steps.

bye

giovanni legnani

===============================================

X-Ph: V4.1@genesis

From: "Tom Lundin"

Date: Tue, 22 Nov 94 11:04:32 EDT

Reply-To:

X-Popmail-Charset: English

To: run1@psu.edu

Subject: cutoff frequencies

Robert,

I have recently encountered a similar problem with filtering motion data.

The best algorithm I could come up with to select a cutoff was to

differentiate the RMS error vs. cutoff frequency twice and search for where

the ensuing curve approximated zero (point Z). I found the slope of the

line described by Winter from the first derivative of the RMS curve at Z.

Then using the equation of that line I found the cutoff frequency as I

presume you already know how to do. If you have any questions or comments

please feel free to write back. I hope this helps and I'll be interested

to see the other responses you receive.

Regards,

Tom Lundin

The Cleveland Clinic Foundation

================================================== ==

X-Ph: V4.1@genesis

From: Paul Guy

Subject: Re: Optimal cutoff frequency for data smoothing

To: run1@psu.edu

Date: Tue, 22 Nov 1994 12:30:55 -0500 (EST)

Content-Length: 4111

Having worked with Dave Winter for many years in his lab, I'll give

you an answer you might not want to hear.

In short, there is no decent mathematical method that I've seen based

on conventional or residual analysis that covers all the situations. If

you are interested in say just the displacements, then a residual

analysis of them will probably do, if you wanted to see what gave the

best results in a power or kinetics situation, then you'd need to do

residuals based on those variables.

The best way to deal with it, is to have some previous knowledge of

the system you are measuring, what its dynamic characteristics are, and

what the behaviour is of the data once it arrives at your computer. Such

things as whether you used interlaced video would be very important

(large 30 hz noise components), or where the resonant frequencies were

on your force plates, transducers etc.

For filtering data from the human body, we will filter different

segments at different frequencies, for example the trunk markers at 1-3

Hz, the foot at 8 to 15 Hz depending on the activity.

Where the accelerations become very important, we find that it's often

worthwhile to raise the sampling frequency, especially if you are doing

stuff like FFT's (and you need long records too). The ratio of cutoff

frequency to sampling frequency will affect whether you are really

getting an analog equivalent. Filtering at 1/4 the sampling frequency

will not give you the characteristics that you might expect.

Another issue is filter TYPE.... are you using Butterworth, Bessel,

IIR,FIR, 2-way pass etc. ? All these become an issue depending on what

you're looking at, in what domain, and how your applications are going

to react to the various 'corruptions'. For example, we use a so-called

4th order 2-way Butterworth (it's run through two 2nd order

Butterworths, the second is filtered backwards in time, to reduce delay

artifacts). Using this filter with force plates causes a force to appear

on the plate before the foot contacts it. That's clearly silly data.

Similiarly, the horizontal impulse the foot gives at heel contact can

really mess up the determination of the body kinetics.....filtering it

can spread what occurs in 10-50ms over a much longer time, rendering

your analysis useless near heel contact.

Don't buy all that theory stuff, sometimes a look at the big picture

will help more.

-Paul

-----------------------------------------------------------------------------

Paul J Guy work phone:519-885-1211 ext 6371

paul@gaitlab1.uwaterloo.ca home/FAX/:519-576-3090

pguy@healthy.uwaterloo.ca 64 Mt.Hope St.,Kitchener,Ontario,Canada

================================================== =

Date: Tue, 22 Nov 1994 11:45:26 -0600 (CST)

X-Ph: V4.1@genesis

From: "Christine Q. Wu"

To: Robert Newton

Subject: Re: Optimal cutoff frequency for data smoothing

Dear Robert: I have the similar problem. Would you please let me know if

you get any solution. Besides, is the range of motion effects the smooth

procedure? If the range of motion is low, may be comparable with the

magnitude of the noise, what will happen?

Good luck!

Christine

================================================== =

Date: 22 Nov 94 16:39:49 EST

X-Ph: V4.1@genesis

From: "Peak Performance Tech."

To: Robert Newton

Subject: Re: Optimal cutoff frequency for data smoothing

Robert-

If you haven't already, you may want to check out the "Jackson Knee

Method". It plots the 2nd derivative of the percent average residual

curve vs. the cutoff frequency. When three points on that curve fall

below a defined prescribed limit, the smallest frequency of the curve

becomes the optimal.

Jackson, K.M. Fitting of mathematical functions to biomechanical data.

IEEE Transactions on Biomedical Engineering, 1979, pp. 122-124.

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George Miller

Peak Performance Technologies

Englewood, CO

76244.3047@CompuServe.com

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Date: Tue, 22 Nov 1994 21:58:37 -0600 (CST)

X-Ph: V4.1@genesis

From: "M. Pizzimenti"

Subject: Re: Optimal cutoff frequency for data smoothing

To: Robert Newton

Robert,

Try Jackson's algorithm where the residuals are differentiated.

Jackson, K.M. Fitting of mathematical functions to biomechanical data.

IEEE Transactions of Biomedical Engineering BME26(2), 122-124, 1979

Hope this helps

Marc Pizzimenti

University of Iowa

Department of Exercise Science

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