====== Second Derivative ======

Compute the second 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:

{{:Second_Derivative.png}}
<code>
Second_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
</code>

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 second derivative is calculated using:

xDDot(ti)= (x(ti+1)-2x(ti)+x(ti-1))/( (ti+1)-(ti) )^2
==== Example: Acceleration of the Center of Mass ====

The Second_Derivative command is useful for calculating the acceleration of targets, landmarks, etc., since acceleration is the second derivative of position. The following example calculates the acceleration of the center of mass by using the Second_Derivative command.

<code>
! 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 acceleration of the center of mass can be computed as follows:
Second_Derivative
/SIGNAL_TYPES=LINK_MODEL_BASED
/SIGNAL_NAMES=COM
! /SIGNAL_FOLDER=ORIGINAL
/RESULT_NAMES=COM_ACCELERATION
/RESULT_TYPES=LINK_MODEL_BASED
/RESULT_FOLDER=ACCELERATION
! /RESULT_SUFFIX=
;
</code>