First Derivative

Compute the first derivative at each point of a signal.

The command can be edited via text editor or via a dialog. The details on the command and the dialog are found below:

First_Derivative /Signal_Types=The type of signal to be evaluated /Signal_Names=The name of the signal to be evaluated /Signal_Folder=The name of the signal folder /Result_Types= The type of the resulting signal /Result_Name= The name of the resulting signal /Result_Folder= The name of the resulting folder /Result_Suffix= The result is given the same name as the original signal with the suffix added

The first and last data points become DATA_NOT_FOUND (identified in the C3D file as a POINT Reliability value of –1).

Calculation Method

Derivatives are calculated using Finite Difference Algorithms.

Given the signal:

x(ti) for i=1, 2, ..., n

The first derivative is calculated using:

xDot(ti)= (x(ti+1)-x(ti-1))/( (ti+1)-(ti-1) )

Example: Velocity of the Centre of Mass

The First_Derivative command is useful for calculating the velocity of targets, landmarks, etc. since velocity is the first derivative of position. The following example calculates the velocity of the center of mass using the First_Derivative command.

! Given a signal representing the center of mass's position as follows:
Compute_Model_Based_Data
/RESULT_NAME=COM
/FUNCTION=MODEL_COG
/SEGMENT=
/REFERENCE_SEGMENT=
! /RESOLUTION_COORDINATE_SYSTEM=LAB
! /USE_CARDAN_SEQUENCE=FALSE
! /NORMALIZATION=FALSE
! /NORMALIZATION_METHOD=
! /NORMALIZATION_METRIC=
! /NEGATEX=FALSE
! /NEGATEY=FALSE
! /NEGATEZ=FALSE
! /AXIS1=X
! /AXIS2=Y
! /AXIS3=Z
;

! The velocity of the center of mass can be computed as follows:
First_Derivative
/SIGNAL_TYPES=LINK_MODEL_BASED
/SIGNAL_NAMES=COM
! /SIGNAL_FOLDER=ORIGINAL
/RESULT_NAMES=COM_VELOCITY
/RESULT_TYPES=LINK_MODEL_BASED
/RESULT_FOLDER=VELOCITY
! /RESULT_SUFFIX=
;