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Order error in the calculation of continuous relative phase.

Sina Mehdizadeh1, Paul S Glazier1

  • 1National Sports Institute of Malaysia, Kuala Lumpur Sports City, Kuala Lumpur, Malaysia.

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This study identifies "order error" in continuous relative phase (CRP) calculations. The Hilbert transform method is recommended for accurate CRP analysis in human movement, surpassing traditional phase-plane portraits.

Keywords:
CoordinationHilbert transformHuman movement kinematicsPhase anglePhase-plane portrait

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Area of Science:

  • Biomechanics
  • Kinematics
  • Signal Processing

Background:

  • Continuous Relative Phase (CRP) is crucial for analyzing coordination in human movement.
  • Conventional methods for calculating CRP can be susceptible to 'order error'.
  • Order error arises from the order of plotting variables in phase-plane portraits, affecting kinematic analysis.

Purpose of the Study:

  • To demonstrate the existence and impact of 'order error' in CRP calculations.
  • To introduce and evaluate two alternative methods for correcting CRP order error.
  • To determine the most effective method for accurate CRP analysis in human movement.

Main Methods:

  • Simulated sinusoidal and non-sinusoidal signals were used to investigate order error.
  • Phase-plane portraits were constructed by plotting position over velocity (alternative method i).
  • The Hilbert transform was applied to calculate CRP (alternative method ii).
  • Human movement kinematic data were analyzed to compare method performance.

Main Results:

  • Order error was confirmed in the conventional CRP calculation method.
  • Both alternative methods successfully corrected order error in simulated data.
  • The Hilbert transform method demonstrated superior performance for human movement data.
  • Phase-plane portraits plotting position over velocity also yielded correct results for simulated signals.

Conclusions:

  • The conventional method for calculating continuous relative phase is prone to order error.
  • Constructing phase-plane portraits with position over velocity and using the Hilbert transform are effective in rectifying order error.
  • The Hilbert transform is the preferred method for accurate CRP calculation in human movement analysis.