The Lowpass Filter command filters a signal's data points using a bidirectional filter. The user can specify whether a BUTTERWORTH or CRITICALLY_DAMPED filter will be used; Visual3D uses a Butterworth Bidirectional Filter for Lowpass/Highpass filtering.

The number of bidirectional passes specified determines the order of the filter (e.g. 1 bidirectional pass results in a fourth order filter). This means if the NUM_BIDIRECTIONAL_PASSES parameter is set to 1, the filter is a fourth order, if the NUM_BIDIRECTIONAL_PASSES parameter is set to two, the filter is an eighth order filter, etc.

For the lowpass filter the slope of the signal is removed before filtering the data, then replaced after filtering.

Lowpass_Filter
! /SIGNAL_TYPES=
! /SIGNAL_FOLDER=ORIGINAL
! /SIGNAL_NAMES=
! /RESULT_FOLDER=PROCESSED
! /RESULT_SUFFIX=
! /FILTER_CLASS=BUTTERWORTH
! /FREQUENCY_CUTOFF=6.0
! /NUM_REFLECTED=6
! /NUM_EXTRAPOLATED=0
! /TOTAL_BUFFER_SIZE=6
! /NUM_BIDIRECTIONAL_PASSES=1
;

The dialog box that can be used to edit the command appears like so:

Explore the changes to the kinematics (e.g. LINK_MODEL_BASED signals) caused by changes to the cutoff frequency. In this example:

1. five cutoff filters (5, 6, 7, 8, and 9 Hz) are applied;
2. The LINK_MODEL_BASED signals are updated; and
3. the LINK_MODEL_BASED signals are copied to a unique folder.

For_Each
/ITERATION_PARAMETER_NAME=CUTOFF
/ITEMS=5+6+7+8+9
;

Lowpass_Filter
/SIGNAL_TYPES=TARGET
! /SIGNAL_NAMES=
! /SIGNAL_FOLDER=ORIGINAL
! /RESULT_SUFFIX=
! /RESULT_FOLDER=PROCESSED
! /FILTER_CLASS=BUTTERWORTH
/FREQUENCY_CUTOFF=::CUTOFF
! /NUM_REFLECTED=6
! /TOTAL_BUFFER_SIZE=6
! /NUM_BIDIRECTIONAL_PASSES=1
;

Recalc
;

Copy_Folder
/SIGNAL_TYPE=LINK_MODEL_BASED
/EXISTING_FOLDER=ORIGINAL
/NEW_FOLDER_NAME=CUTOFF&::CUTOFF
/OVERWRITE_EXISTING_SIGNALS=TRUE
;

End_For_Each
/ITERATION_PARAMETER_NAME=CUTOFF
;

The procedure filters the input data from the first good frame of data to the last good frame of data (according to POINT Reliability - fourth component of the POINT signal in the data tree). The leading and trailing data are ignored.

Digital filters do not work particularly well at the ends of the data array. In an attempt to minimize this problem, Visual3D's procedure buffers the data at both ends.

Num_Buffered_Frames:

The user can specify that the data be reflected at the beginning and end of the array and/or that the data be linearly extrapolated at the beginning and end of the array.

Num_Reflected_Frames:

Num_Extrapolate_Frames:

For example, if 10 points are reflected and the total size of the buffer is set to 20, then 10 points will be reflected at the beginning and end of the signal and 10 additional frames of data will be extrapolated linearly beyond this. After the data is filtered, the buffer is deleted.

The cutoff frequency takes into account the number of bidirectional passes through the signal. The default lowpass filter in Visual3D is a fourth order Butterworth filter.

Butterworth filters have an upper limit on the magnitude of the cutoff frequency. The maximum theoretical cutoff frequency is

sampling_rate*0.802/2

. Visual3D is a little more conservative than that because we have found the filter to be unreliable at the theoretical limits. The highest cutoff frequency that Visual3D will allow you is

0.393 * sampling-rate

For example, if your EMG signals are sampled at 1000 Hz, then the highest cutoff frequency you can implement in Visual3D is 393 Hz.

Note that the cutoff frequency can be specified as an expression. For example, consider that the signal to be filtered is an ANALOG signal:

/Frequency_Cutoff= 0.393*METRIC::PROCESSED::ANALOG_RATE

Robertson DGE and Dowling JJ (2003) Design and responses of Butterworth and critically dampted digital filters. Journal of Electromyography and Kinesiology 13. 569-573

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