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Table 3 Proposed methods to process different types of measured movement related variables before applying the SPARC or LDLJ measures

From: On the analysis of movement smoothness

Measured movement variable x (t) Proposed processing for SPARC and LDLJ Rationale
Movement kinematics - position (in either task or joint space) through motion capture system or other position sensors SPARC: Use speed, \(\lVert \frac {d\mathbf {x}(t)}{dt} \rVert _{2}\) Speed highlights intermittencies, and does not amplify noise as much as the other higher order derivatives.
  LDLJ: Use jerk magnitude, \(\lVert \frac {d^{3}\mathbf {x}(t)}{dt^{3}} \rVert _{2}\) This is by definition.
Movement kinematics - acceleration measured by an accelerometer SPARC: Use gravity subtracted absolute magnitude of acceleration, \(\left |\lVert \mathbf {x}(t) \rVert _{2} - g\right |\) Accelerometers also pick up gravity, and this must be removed to apply the SPARC, otherwise this would lead to a large DC component in the spectrum, which will dominate the other spectral components. This proposed method is based on our unpublished prior work on estimating smoothness from accelerometers. It must be noted that here the SPARC is used on signals from the acceleration space, and not the velocity space, as was done with position information.
  LDLJ: Use magnitude of jerk, \(\lVert \frac {d\mathbf {x}(t)}{dt} \rVert _{2}\) This is by definition. Simply derive the jerk from the accelerometer data.
Force, Torque or impedance SPARC: Use the magnitude of first derivative of force/toque, \(\lVert \frac {d\mathbf {x}(t)}{dt} \rVert _{2}\) The proposed method for SPARC and LDLJ are based on the treating these variables like position variables. This suggestion is purely based on intuition, and must be verified through future experiments.
  LDLJ: Use the magnitude of third derivative of force/torque, \(\lVert \frac {d^{3}\mathbf {x}(t)}{dt^{3}} \rVert _{2}\)