Endpoint error in smoothing and differentiating raw kinematic data

An evaluation of four popular methods

Peter F. Vint, Richard N. Hinrichs

Research output: Contribution to journalArticle

40 Citations (Scopus)

Abstract

'Endpoint error' describes the erratic behavior at the beginning and end of the computed acceleration data which is commonly observed after smoothing and differentiating raw displacement data. To evaluate endpoint error produced by four popular smoothing and differentiating techniques, Lanshammar's modification of the Pezzack et al. raw angular displacement data set was truncated at three different locations corresponding to the major peaks in the criterion acceleration curve. Also, for each data subset, three padding conditions were applied. Each data subset was smoothed and differentiated using the Butterworth digital filter, cubic spline, quintic spline, and Fourier series to obtain acceleration values. RMS residual errors were calculated between the computed and criterion accelerations in the endpoint regions. Although no method completely eliminated endpoint error, the results demonstrated clear superiority of the quintic spline over the other three methods in producing accurate acceleration values close to the endpoints of the modified Pezzack el al. data set. In fact, the quintic spline performed best with non-padded data (cumulative error = 48.0 rad s-2). Conversely, when applied to non-padded data, the Butterworth digital filter produced wildly deviating values beginning more than the 10 points from the terminal data point (cumulative error = 226.6 rad s-2). Each of the four methods performed better when applied to data subsets padded by linear extrapolation (average cumulative error = 68.8 rad s-2) than when applied to analogous subsets padded by reflection (average cumulative error = 86.1 rad s-2).

Original languageEnglish (US)
Pages (from-to)1637-1642
Number of pages6
JournalJournal of Biomechanics
Volume29
Issue number12
DOIs
StatePublished - Dec 1996

Fingerprint

Biomechanical Phenomena
Kinematics
Splines
Butterworth filters
Digital filters
Fourier Analysis
Fourier series
Set theory
Extrapolation
Datasets

Keywords

  • Data padding
  • Differentiation
  • Endpoint error
  • Smoothing

ASJC Scopus subject areas

  • Orthopedics and Sports Medicine

Cite this

Endpoint error in smoothing and differentiating raw kinematic data : An evaluation of four popular methods. / Vint, Peter F.; Hinrichs, Richard N.

In: Journal of Biomechanics, Vol. 29, No. 12, 12.1996, p. 1637-1642.

Research output: Contribution to journalArticle

Vint, Peter F. ; Hinrichs, Richard N. / Endpoint error in smoothing and differentiating raw kinematic data : An evaluation of four popular methods. In: Journal of Biomechanics. 1996 ; Vol. 29, No. 12. pp. 1637-1642.
@article{02018db4e39f41c5a45659efa0e1b22f,
title = "Endpoint error in smoothing and differentiating raw kinematic data: An evaluation of four popular methods",
abstract = "'Endpoint error' describes the erratic behavior at the beginning and end of the computed acceleration data which is commonly observed after smoothing and differentiating raw displacement data. To evaluate endpoint error produced by four popular smoothing and differentiating techniques, Lanshammar's modification of the Pezzack et al. raw angular displacement data set was truncated at three different locations corresponding to the major peaks in the criterion acceleration curve. Also, for each data subset, three padding conditions were applied. Each data subset was smoothed and differentiated using the Butterworth digital filter, cubic spline, quintic spline, and Fourier series to obtain acceleration values. RMS residual errors were calculated between the computed and criterion accelerations in the endpoint regions. Although no method completely eliminated endpoint error, the results demonstrated clear superiority of the quintic spline over the other three methods in producing accurate acceleration values close to the endpoints of the modified Pezzack el al. data set. In fact, the quintic spline performed best with non-padded data (cumulative error = 48.0 rad s-2). Conversely, when applied to non-padded data, the Butterworth digital filter produced wildly deviating values beginning more than the 10 points from the terminal data point (cumulative error = 226.6 rad s-2). Each of the four methods performed better when applied to data subsets padded by linear extrapolation (average cumulative error = 68.8 rad s-2) than when applied to analogous subsets padded by reflection (average cumulative error = 86.1 rad s-2).",
keywords = "Data padding, Differentiation, Endpoint error, Smoothing",
author = "Vint, {Peter F.} and Hinrichs, {Richard N.}",
year = "1996",
month = "12",
doi = "10.1016/0021-9290(96)00079-6",
language = "English (US)",
volume = "29",
pages = "1637--1642",
journal = "Journal of Biomechanics",
issn = "0021-9290",
publisher = "Elsevier Limited",
number = "12",

}

TY - JOUR

T1 - Endpoint error in smoothing and differentiating raw kinematic data

T2 - An evaluation of four popular methods

AU - Vint, Peter F.

AU - Hinrichs, Richard N.

PY - 1996/12

Y1 - 1996/12

N2 - 'Endpoint error' describes the erratic behavior at the beginning and end of the computed acceleration data which is commonly observed after smoothing and differentiating raw displacement data. To evaluate endpoint error produced by four popular smoothing and differentiating techniques, Lanshammar's modification of the Pezzack et al. raw angular displacement data set was truncated at three different locations corresponding to the major peaks in the criterion acceleration curve. Also, for each data subset, three padding conditions were applied. Each data subset was smoothed and differentiated using the Butterworth digital filter, cubic spline, quintic spline, and Fourier series to obtain acceleration values. RMS residual errors were calculated between the computed and criterion accelerations in the endpoint regions. Although no method completely eliminated endpoint error, the results demonstrated clear superiority of the quintic spline over the other three methods in producing accurate acceleration values close to the endpoints of the modified Pezzack el al. data set. In fact, the quintic spline performed best with non-padded data (cumulative error = 48.0 rad s-2). Conversely, when applied to non-padded data, the Butterworth digital filter produced wildly deviating values beginning more than the 10 points from the terminal data point (cumulative error = 226.6 rad s-2). Each of the four methods performed better when applied to data subsets padded by linear extrapolation (average cumulative error = 68.8 rad s-2) than when applied to analogous subsets padded by reflection (average cumulative error = 86.1 rad s-2).

AB - 'Endpoint error' describes the erratic behavior at the beginning and end of the computed acceleration data which is commonly observed after smoothing and differentiating raw displacement data. To evaluate endpoint error produced by four popular smoothing and differentiating techniques, Lanshammar's modification of the Pezzack et al. raw angular displacement data set was truncated at three different locations corresponding to the major peaks in the criterion acceleration curve. Also, for each data subset, three padding conditions were applied. Each data subset was smoothed and differentiated using the Butterworth digital filter, cubic spline, quintic spline, and Fourier series to obtain acceleration values. RMS residual errors were calculated between the computed and criterion accelerations in the endpoint regions. Although no method completely eliminated endpoint error, the results demonstrated clear superiority of the quintic spline over the other three methods in producing accurate acceleration values close to the endpoints of the modified Pezzack el al. data set. In fact, the quintic spline performed best with non-padded data (cumulative error = 48.0 rad s-2). Conversely, when applied to non-padded data, the Butterworth digital filter produced wildly deviating values beginning more than the 10 points from the terminal data point (cumulative error = 226.6 rad s-2). Each of the four methods performed better when applied to data subsets padded by linear extrapolation (average cumulative error = 68.8 rad s-2) than when applied to analogous subsets padded by reflection (average cumulative error = 86.1 rad s-2).

KW - Data padding

KW - Differentiation

KW - Endpoint error

KW - Smoothing

UR - http://www.scopus.com/inward/record.url?scp=0030560685&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030560685&partnerID=8YFLogxK

U2 - 10.1016/0021-9290(96)00079-6

DO - 10.1016/0021-9290(96)00079-6

M3 - Article

VL - 29

SP - 1637

EP - 1642

JO - Journal of Biomechanics

JF - Journal of Biomechanics

SN - 0021-9290

IS - 12

ER -