Discrete wavelet transform

A tool in smoothing kinematic data

Adham R. Ismail, Shihab S Asfour

Research output: Contribution to journalArticle

45 Citations (Scopus)

Abstract

Motion analysis systems typically introduce noise to the displacement data recorded. Butterworth digital filters have been used to smooth the displacement data in order to obtain smoothed velocities and accelerations. However, this technique does not yield satisfactory results, especially when dealing with complex kinematic motions that occupy the low- and high- frequency bands. The use of the discrete wavelet transform, as an alternative to digital filters, is presented in this paper. The transform passes the original signal through two complementary low- and high-pass FIR filters and decomposes the signal into an approximation function and a detail function. Further decomposition of the signal results in transforming the signal into a hierarchy set of orthogonal approximation and detail functions. A reverse process is employed to perfectly reconstruct the signal (inverse transform) back from its approximation and detail functions. The discrete wavelet transform was applied to the displacement data recorded by Pezzack et al., 1977. The smoothed displacement data were twice differentiated and compared to Pezzack et al.'s acceleration data in order to choose the most appropriate filter coefficients and decomposition level on the basis of maximizing the percentage of retained energy (PRE) and minimizing the root mean square error (RMSE). Daubechies wavelet of the fourth order (Db4) at the second decomposition level showed better results than both the biorthogonal and Coiflet wavelets (PRE = 97.5%, RMSE = 4.7 rad s-2). The Db4 wavelet was then used to compress complex displacement data obtained from a noisy mathematically generated function. Results clearly indicate superiority of this new smoothing approach over traditional filters.

Original languageEnglish
Pages (from-to)317-321
Number of pages5
JournalJournal of Biomechanics
Volume32
Issue number3
DOIs
StatePublished - Mar 1 1999

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Wavelet Analysis
Discrete wavelet transforms
Biomechanical Phenomena
Kinematics
Noise
Digital filters
Decomposition
Mean square error
Butterworth filters
High pass filters
Inverse transforms
FIR filters
Frequency bands

Keywords

  • Kinematic
  • Signal compression
  • Signal smoothing
  • Wavelets

ASJC Scopus subject areas

  • Orthopedics and Sports Medicine

Cite this

Discrete wavelet transform : A tool in smoothing kinematic data. / Ismail, Adham R.; Asfour, Shihab S.

In: Journal of Biomechanics, Vol. 32, No. 3, 01.03.1999, p. 317-321.

Research output: Contribution to journalArticle

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