# Mathematical Morphological Filter (G Dataflow)

Version:

Filters a signal with a specific structure element using a mathematical morphological filter.

## extension type

Method by which to extend the input signal at both ends of the sequence.

Name Value Description
Zero padding 0 Extends the input signal by padding zeros at both ends of the original signal.
Symmetric 1 Extends the input signal to form a new sequence that is symmetric at both ends of the original signal.
Periodic 2 Extends the input signal to form a new sequence that is periodic at both ends of the original signal.

Filtering a Signal with the Zero Padding Method

The following illustration represents the output sequence when extension type is Zero padding.

Where X is the input signal, and k is the length of structure element.

Filtering a Signal with the Symmetric Method

The following illustration represents the output sequence when extension type is Symmetric.

Where X is the input signal, and k is the length of structure element.

If k > n, this node pads X with k - n zeros at both ends of the new sequence, where n is the length of X.

Filtering a Signal with the Periodic Method

The following illustration represents the output sequence when extension type is Periodic.

Where X is the input signal, and k is the length of structure element.

If k > n, this node periodically repeats X more than once at both ends of the sequence.

## signal

The input signal.

## structure element

Structure element to use in the filtering process.

## operation type

Fundamental operation of the morphological filter.

Name Value Description
Dilation 0 Specifies to perform dilation on the input signal.
Erosion 1 Specifies to perform erosion on the input signal.

Algorithm and Example for the Dilation Operation

The dilation of a 1D signal f is defined as follows:

$D\left(i\right)=\mathrm{max}\left\{x\left(i-j\right)+s\left(j\right)\right\},\text{\hspace{0.17em}}\text{\hspace{0.17em}}0\le i\le n-1,\text{\hspace{0.17em}}0\le j\le k-1$

where x(i) is the i-th element in the input signal and s(j) is the j-th element in structure element.

The following image shows an example of the dilation effect. The original signal consists of two pulses with widths of 20, and the structure element is an array of ten zeros. The filtered signal expands the pulses in the original signal.

Algorithm and Example for the Erosion Operation

The erosion of a 1D signal f is defined as follows:

$E\left(i\right)=\mathrm{min}\left\{x\left(i+j\right)-s\left(j\right)\right\},\text{\hspace{0.17em}}\text{\hspace{0.17em}}0\le i\le n-1,\text{\hspace{0.17em}}0\le j\le k-1$

where x(i) is the i-th element in the input signal and s(j) is the j-th element in structure element.

The following image shows an example of the erosion effect. The original signal consists of two pulses with widths of 20, and the structure element is an array of ten zeros. The filtered signal shrinks the pulses in the original signal.

Default: Dilation

## zero phase?

A Boolean that specifies whether to perform zero-phase filtering of the signal.

 True Performs zero-phase filtering of the signal. False Does not perform zero-phase filtering of the signal.

Default: True

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error

## filtered signal

Filtered signal.

## error out

Error information. The node produces this output according to standard error behavior.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported