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Digital Filter Cutoff Frequencies for GRF Data - Summary

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  • Digital Filter Cutoff Frequencies for GRF Data - Summary

    Hello All,
    Thank you to all that responded to my posting. I have attached all
    responses below. I think that there were many good issues brought up in the
    responses, including some alternatives for optimal filtering methodologies.
    For my problem, in consultation with Peter Vint and taking into
    account many of the responses, it was decided to select a single cutoff
    frequency at which to filter all of the data. FFT analyses were performed on
    the worst case (i.e. highest running speed) trials. It was found that 99% of
    the signal power for all of the trials (8 footfalls per trials = 48 total
    footfalls analyzed) were at frequencies below 40 Hz. Using that rationale,
    it was decided to filter all data at 40 Hz. In addition, all data sets are
    being padded at the front and back with zeros to alleviate endpoint issues.
    Preliminary processing is revealing that this cutoff frequency is sufficient
    to remove random noise, but to also maintain the integrity of the signal.
    I did find a couple of issues through the process that may be of
    interest that occur with the Challis (1999) algorithm.
    1) If the Challis algorithm is run on data that is not padded, a different
    cutoff frequency may be selected than if that data set were padded.
    2) The Challis algorithm will select different cutoff frequencies depending
    upon which data are used during the auto correlation.

    It is my suggestion that when using the Challis algorithm (which, by the
    way, I feel is a very good algorithm), authors should pad their data, and if
    the entire dataset is not used to determine the optimal cutoff frequency, it
    should be noted in the methods. An example of this case would be just using
    the propulsive phase of the GRF instead of the entire GRF trajectory when
    using the algorithm.

    In any case, here are the responses:
    ================================================== =========================
    Hi John

    I'm interested in your question for two reasons, (I) I will be collecting
    ground reaction force data in the KC135 (for a jumping study) in less than 2
    weeks's time, and (ii) for other studies, I am very involved in collecting
    3D ground reaction forces using instrumented treadmills.

    In the case of your data, would it make sense to treat each phase of the
    ground contact differently? For instance, if you were interested in the
    peak push off force, the method of Challis would seem to be perfectly
    acceptable, since the initial transient at heal strike would not matter.
    If, in addition, you wanted to know the timing and magnitude of the initial
    transient, it might help to isolate your data for the first 0.05 seconds and
    then either (a) subject this window to Challis' method or (b) simply
    superimpose many trials on top of each other to ascertain whether there is a
    transient force. I realize there are disadvantages with the latter, but the
    advantage is that the vibrations due to the KC135 may cancel each other out
    (assuming there was no synchronization between the KC135's vibrations and
    the timing of footstrike events), and you would be left with some indication
    of a heelstrike transient.

    Regards, Brian -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
    Brian L. Davis, Ph.D.
    Department of Biomedical Engineering (ND20)
    Cleveland Clinic Foundation

    ================================================== =========================
    Hi John

    What I meant was that you don't need the whole contact phase if you want to
    focus on the heel transients. Likewise, you don't need the transient
    portion if you are interested in peak push off forces. You could break the
    data into two pieces---and treat each piece differently.

    Regards, Brian -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
    Brian L. Davis, Ph.D.
    Department of Biomedical Engineering (ND20)
    Cleveland Clinic Foundation

    ================================================== =========================
    Hi John
    we face similar questions with our force-treadmill data collected on Earth.
    obviously the vibration of the treadmill motor is not what we want to

    my student Jinger Gottschall has written some Matlab code to
    successively filter the data at decreasing cut offs and chart the
    effect on the average impact peaks.
    obviously, the lower the cut off the lower the impact peaks. so i
    would filter at the "elbow" frequency where above it, there is no
    dimunition of the peaks.
    i have asked Jinger to contact you, but she is away next week and she
    is trying to finish her PhD.

    rather than rely on a generic algorithm, i would: collect the same
    data for one subject on Earth (if possible). compare the noisy KC 135
    data and the clean Earth data. that will tell you what you are
    looking for. i would then FFT both data sets. the real FFT peaks
    should show up on both data sets, the other FFT peaks are noise. that
    should help you to decide how to filter it.

    you might check out my paper on our older force treadmill. we talk
    about this filteringn decision process.
    R. Kram, T.M. Griffin, J.M. Donelan, Y.H. Chang. Force-treadmill for
    measuring vertical and horizontal ground reaction forces. J. Applied
    Physiology 85: 764-769, 1998.
    you can download the paper from my web site listed below.
    We have built a new force treadmill that has two belts and thus can
    record individual foot forces in walking.

    So, what was the KC-135 experiment? As you probably know my
    colleague Young Hui Chang and I have thought about impact forces in
    hypo-gravity. Y.-H. Chang, C. M. Hamerski and R. Kram. Applied
    horizontal force increases impact loading in reduced gravity running.
    J. Biomechanics. 34:679-685, 2001.


    Rodger Kram, Ph.D.
    Associate Professor
    Dept. of Integrative Physiology
    Univ. of Colorado
    354 UCB
    Boulder, CO 80309-0354

    ================================================== =========================
    Hi Mr DeWitt,

    I think you have a great application for using wavelet
    filtering. I would use the review from Chau as a starting

    Good luck!
    Michel Ladouceur, PhD
    ================================================== =========================
    Dear Dr. DEWITT,
    in the '90s I presented an automatic digital filtering procedure named
    LAMBDA based on the automatic identification from the noisy signal of both
    signal and frequency content. This method determines an optimal (in some
    sense) filtering frequency cut-off taking into account signal and noise
    characteristics. In this period I'm going to present a new enhanced version
    of LAMBDA procedure that is applicable even to not equispaced samples. Given
    the fact there are a lot of considerations about signal sampling frequency,
    signal frequency content and noise frequency content and level, before
    entering into more detailed theoretical discussion about signal filtering
    and derivatives assessment, I think You could send me a copy of the signals
    You need to process in ASCII format specifying at the first line the signal
    sampling frequency. I shall process these data for You with such new method
    and I shall enter in further considerations once I'll get access to signals

    [1] M. D'Amico and G. Ferrigno: Technique for the Evaluation of Derivatives
    from Noisy Biomechanical Displacement Data Using a Model-Based
    Bandwidth-Selection Procedure, Med. & Biol. Eng. & Comput. 28, pp.407-415,
    1990. [2] M. D'Amico and G. Ferrigno, Comparison between the More Recent
    Techniques for Smoothing and Derivative Assessment in Biomechanics, Med. &
    Biol. Eng. & Comput. 30, pp. 193-204, 1992. Dr. Ing. MORENO D'AMICO
    65124 Pescara Sede Operativa Via Aterno 154 (giĆ  Via Salara 7) 66020 San
    Giovanni Teatino (CH) C.F. - P. IVA 01457770681 Tel. (+39) 085-4463940
    Fax: (+39) 085-4408450
    ================================================== =========================

    I'm not familiar with this specific problem, but just wanted to offer a
    concern about using different filters for distinct data sets. If you filter
    causally, then different filter cutoffs will produce different phase delays.
    Thus, differences in timing in the filtered signal can be the result of
    changes in the cutoff frequency location. Thus, real changes could be
    masked. So. I'd recommend either (1) demonstrating that the range of filters
    that you would use have sufficiently similar phase responses, or (2) use
    zero-phase, non-causal filtering to avoid this particular issue (e.g., see
    "filtfilt()" in MATLAB).

    Best of luck,

    Ted Clancy

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

    I have measured GRF from Gaitway treadmill for the purpose of simulating
    effects of walking on floors of wafer-fab facilities.
    For that I need up to 30Hz. The walking data and some frequency information
    are in Candadian journal of civil engineering online 2004, I have a copy
    somewhere. Essentially for walking/running the sequence of harmonics goes on
    almost indefinitely so for say 2Hz walking (fpacing rate) you could take 6
    to 8 times that.

    Actually For civil dynamics of high frequency floors we find that a
    footfall, e.g. heelstrike works like an impulse with frequency content
    dropping off quite fast, as the pulse is wide.

    I don't follow any of the procedures you mention but it is clear from the
    GRF auto spectra that energy diminishes rapidly above 30Hz.

    I have used 200Hz sample rate but for time history calulcation would be
    happy to downsample to 100Hz, retaining information up to 40Hz zero

    Not sure if this helps ...

    Until Feb 14th I am .....

    James M W Brownjohn
    Associate Professor,
    Division of Structures and Mechanics,
    School of Civil and Environmental Engineering,
    Nanyang Technological University,
    50 Nanyang Avenue,
    SINGAPORE 639798
    Tel +65 67904773
    Fax +65 67910676

    After that you can still reach me by this e-mail for a while but my postal
    address will be:

    James M W Brownjohn
    Professor of Structural Engineering
    School of Engineering
    University of Plymouth
    Drake Circus
    Plymouth PL4 8AA
    United Kingdom
    ================================================== =========================
    My preferred method for determining the appropriate cut-off frequency is
    found in:

    Yu, B., Gabriel, D., Noble, L., and Kai-Nan, A. (1999) Estimate of the
    Optimum Cut-off Frequency for the Butterworth Low-Pass Digital Filter.
    Journal of Applied Biomechanics, 15(3), 318-329.

    I have used this method for many years and it usually chooses a rather high
    cut-off frequency leaving a lot if the signal while eliminating much of the
    noise. I have a Matlab routine that applies this method, if you are


    Tim Doyle
    Edith Cowan University
    PhD Candidate - Biomechanics
    Perth, WA, Australia
    +61 411 551 744 (Mobile/Cell)
    +61 8 9400 5097 (Office)

    ================================================== =========================
    Dear John,
    I would suggest to find once and for all a suitable cut-off frequency,
    and then stick to it.
    In this way you have data sets which are mutually comparable.
    This is better than squeezing all information out of any available
    The choice of the cut-off depends on your application. In this
    aspect I am against so-called objective criteria, as Challis' is
    probably one. It is, for example, advisable to use the same cut-off
    frequency (often 3-6 Hz) for the force plate data as for the
    kinematics, when you do inverse dynamics (see discussion on

    The worst case I ever saw was commercial software for kinematics,
    in which x, y and z coordinates were all filtered with different
    'optimal' cut-off frequencies, one by one determined with a very
    clever algorithm.

    These were my subjective opinions. Yours,

    At Hof
    Institute of Human Movement Science
    University of Groningen
    PO Box 196
    9700 AD Groningen
    The Netherlands
    Tel: (31) 50 363 2645

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

    Hello John,

    I was reading thru your question on Challis' method to determine the cutoff
    frequency. I am not familiar with his method, but I am familiar with the
    lowpass filter that he is using. My initial guess after reading the abstract
    of his method is that it is iteratively computing the the error between the
    filtered signal and non-filtered signal and changing the cutoff frequency
    until the error obtained is minimal.

    I have done a bit of signal processing with regards to images and I wouldn't
    mind discussing it with you. I have requested a copy of his article so I
    could learn about his method.

    Just a thought:

    In his work, he has determined the cutoff frequency using the
    characteristics of white noise as a reference. I am not fully aware of the
    type of signal you are acquiring, but, will it help to do a dry-run and use
    that as a reference to determine the cutoff frequency?

    dry-run: Collect data without taking the airplane for a parabolic cycle i.e.
    collect treadmill data without take-off. Use that as the ideal signal
    characteristic and identify the cut-off freq accordingly. This will help you
    to isolate the noise components due to the motion of the plane, and then you
    will just have to deal with general noise in the signal.

    Will this help???



    Archana P. Sangole, Ph.D.
    Engineering Postdoctoral Fellow
    Rehabilitation Sciences and Orthopaedics
    The University of Texas Medical Branch
    Mail Route #0892
    Tel: (409) 747-4545
    Fax: (409) 747-4223

    ================================================== =========================
    Hi John:

    When I have processed noisy GRF data, I have done the calculations and the
    identification of critical points using unfiltered data, and have just
    filtered for "presentation" purposes. This idea probably comes from the
    processing of EMG data. Filtered GRF curves may look right, but I don't
    think that there is any real way of knowing what is correct for each
    subject. Unless your data are so noisy that you are getting unrealistic
    peak values, I would suggest finding important points such as maxima from
    the unfiltered data.

    If you do decide to filter the data, it would likely be very difficult to
    convince reviewers that filtering some trials one way, and other trials with
    another method would be acceptable. Although I agree that this is probably
    the best solution if it is done well, and with integrity, as you would do,
    it also leads to the perception that the data could have been "fudged."

    Hope this helps.

    Al Hreljac

    ================================================== =========================
    Dear Mr Dewitt,

    My collegue has forwarded me your e-mail, regarding the selection of an
    appropriate cuttoff frequency. My name is Radmila Maksimovic, and I'm a PhD
    student at King's College, London. The subject of my thesis is detection and
    prediction of epileptic seizures through non-invasive evaulation of body
    moevemnts and cardiac parameters. Seems to me that I have very similar
    problem to yours: namely, I am trying to remove the aretfact (noise) and to
    extract the QRS peak frequency, which is corrupted in that noise. Using the
    4th order Butterworth filter I was not able to distinguish it from the noise
    (you seem to have the same problem with an impact peak). I also agree with
    you in the thing that you have to use various methods for determination of
    the cuttoff frequency. In my case heart rate varies a lot from patient to
    patient and different cuttoff frequencies have to be used anyway. I would be
    interested to try Challis approach on my data and would be very grateful if
    you could send me the algorithm you use - so, we can make the conclusions
    for different data.Look forward to hearing from you.

    Best regards,
    Radmila Maksimovic

    ================================================== =========================
    Dear John,
    You ask a great question with which I have struggled lately. My colleagues
    and I have been developing analyses in Matlab to study hip and pelvis
    synchronization and kinematics. We are identifying characteristics that may
    distinguish movement patterns in persons with and without low back pain. One
    task has subjects laying face-down, bending hip and knee, and trying to
    rotate only at the hip while preventing motion at the pelvis and the knee.
    Subjects chose their own paces, so movement times in one direction ranged
    from 1 to 6 seconds. We are particularly interested in the start of pelvic
    movement relative to hip, but the pelvic movements were generally small and
    did not vary consistently through a trial. Hence, we thought a lot about
    finding a good filtering strategy and start-end of motion algorithm.
    Smoothing the data with a dualpass butterworth 4th order filter resulted in
    a fairly significant oversmoothing/undersmoothing tradeoff when we chose a
    single cutoff (attenuation) frequency across subjects with different
    movement times. We decided on a two-pass filtering procedure. In the first
    pass, the raw data was filtered at 2.5Hz, and the primary hip angle
    (transverse rotation) was used to determine the start and end of motion. A
    period of movement was estimated as twice the movement time, from which a
    trial-specific frequency cutoff was determined as 1/(.15*period), e.g. a
    movement time of 2s yields a cutoff of 1/(.15*4)=1.67Hz. This ratio was
    developed in part from the discussion in Dr. Winter's text.
    We then filtered the raw hip and pelvic angles with the trial-specific
    cutoff, determined angular velocities, and calculated start and end of
    motion for hip and pelvis angles from an algorithm using both angle and
    velocity. The objective algorithm agreed with our subjective visual
    assessments of start and end of motion for over 99% of the data). However,
    the filtering itself seemed a little high or low for 10-15% of the data
    (oversensitive to the trial-specific cutoff frequencies), so we may revise
    this procedure somewhat. We look forward to your summary for possible
    improvements and opposing opinions.
    Dave Collins, PhD, Washington University School of Medicine, St. Louis, MO,
    ================================================== =========================
    Dear John,
    In your recent email to biomch-l you describe problems you are having
    selecting a filter cut-off frequency for processing ground reaction force
    data collected from a treadmill. In principle it makes sense to use
    different cut-off frequencies for different data sets as the signal to noise
    content varies depending on the measurement equipment and the signal
    generated by each subject.

    Methods which automatically determine the cut-off frequency (or amount of
    smoothing) effectively make a judgment about the signals signal-to-noise
    ratio; typically assuming the noise is white. White noise has a flat power
    spectrum, and is present across all frequencies. In the case you are
    examining, treadmill ground reaction force data, I suspect the natural
    frequency of your measurement equipment is generating noise which is not
    white, thus violating one of the assumptions of automatic methods. This
    combined with the impact peak in the ground reaction force data being of a
    much higher frequency than the rest of the ground reaction force signal,
    makes appropriate filtering of ground reaction force data with an automatic
    method problematic.

    I would be happy to look at some of your data, for example you could send me
    example trials on which the automated procedure works and some on which it
    does not work.


    John H. Challis, Ph.D.
    Center for Locomotion Studies
    29, Recreation Building
    The Pennsylvania State University
    University Park

    John DeWitt, M.S., C.S.C.S.
    Biomechanist - Exercise Physiology Laboratory
    Space Physiology & Countermeasures
    NASA - Johnson Space Center
    Houston, TX 77058
    281-483-8939 / 281-483-4181 (fax)

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