# Convolution (G Dataflow)

Computes the convolution of two sequences.  ## reset

A Boolean that specifies whether to reset the internal state of the node.

 True Resets the internal state of the node. False Does not reset the internal state of the node.

This input is available when either of the input sequences is a double-precision, floating-point number, a waveform, or an array of waveforms.

Default: False ## x

The first input sequence.

This input accepts the following data types:

• Waveform
• Double-precision, floating-point number
• 1D array of waveforms
• 1D array of double-precision, floating-point numbers
• 1D array of complex double-precision, floating-point numbers
• 2D array of double-precision, floating-point numbers
• 2D array of complex double-precision, floating-point numbers ## y

The second input sequence.

This input accepts the following data types:

• Waveform
• Double-precision, floating-point number
• 1D array of waveforms
• 1D array of double-precision, floating-point numbers
• 1D array of complex double-precision, floating-point numbers
• 2D array of double-precision, floating-point numbers
• 2D array of complex double-precision, floating-point numbers ## sample length x

Length of each set of x-values. This node computes each set of values separately.

sample length x must be greater than 0.

This input is available only if x is a double-precision, floating-point number.

Default: 100 ## sample length y

Length of each set of y-values. This node computes each set of values separately.

sample length y must be greater than 0.

This input is available only if y is a double-precision, floating-point number.

Default: 100 ## algorithm

The convolution method to use.

This input is available only if x and y are waveforms or arrays.

If x and y are small, the direct method typically is faster. If x and y are large, the frequency domain method typically is faster. Additionally, slight numerical differences can exist between the two methods.

Name Description
frequency domain

Computes the convolution using an FFT-based technique.

direct

Computes the convolution using the direct method of linear convolution.

Computing 1D Convolution with the Frequency Domain Method

When algorithm is frequency domain, this node completes the following steps to compute the linear convolution:

1. Pads the end of x and y with zeros to make their lengths M + N - 1, as shown in the following equations.
${x\prime }_{i}=\left\{\begin{array}{cc}{\begin{array}{c}x\end{array}}_{i}& i=0,\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}N-1\\ 0& i=N,\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}M+N-2\end{array}$
${y\prime }_{i}=\left\{\begin{array}{cc}{y}_{i}& i=0,\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}M-1\\ 0& i=M,\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}M+N-2\end{array}$
2. Calculates the Fourier transform of x' and y' according to the following equations.
$x\prime \left(f\right)=FFT\left(x\prime \right)$
$y\prime \left(f\right)=FFT\left(y\prime \right)$
3. Multiplies x'(f) by y'(f) and calculates the inverse Fourier transform of the product. The result is the linear convolution of x and y, as shown in the following equation.
$x*y=IFFT\left(x\prime \left(f\right)\cdot y\prime \left(f\right)\right)$

Computing 2D Convolution with the Frequency Domain Method

When algorithm is frequency domain, this node completes the following steps to compute the two-dimensional convolution:

1. Pads the end of x and y with zeros to make their sizes (M1 + M2 - 1)-by-(N1 + N2 - 2), as shown in the following equations.
${x\prime }_{ij}=\left\{\begin{array}{cc}{\begin{array}{c}x\end{array}}_{ij}& i=0,\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}{M}_{1}-1,\text{\hspace{0.17em}}j=0,\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}{N}_{1}-1\\ 0& i={M}_{1},\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}{M}_{1}+{M}_{2}-2,\text{\hspace{0.17em}}j={N}_{1},\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}{N}_{1}+{N}_{2}-2\end{array}$
${y\prime }_{ij}=\left\{\begin{array}{cc}{\begin{array}{c}y\end{array}}_{ij}& i=0,\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}{M}_{2}-1,\text{\hspace{0.17em}}j=0,\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}{N}_{2}-1\\ 0& i={M}_{2},\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}{M}_{1}+{M}_{2}-2,\text{\hspace{0.17em}}j={N}_{2},\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}{N}_{1}+{N}_{2}-2\end{array}$
2. Calculates the Fourier transform of x' and y' according to the following equations.
$x\prime \left(f\right)=FFT\left(x\prime \right)$
$y\prime \left(f\right)=FFT\left(y\prime \right)$
3. Multiplies x'(f) by y'(f) and calculates the inverse Fourier transform of the product. The result is the two-dimensional convolution of x and y, as shown in the following equation.
$x*y=IFFT\left(x\prime \left(f\right)\cdot y\prime \left(f\right)\right)$

Computing 1D Convolution with the Direct Method

When algorithm is direct, this node uses the following equation to perform the discrete implementation of the linear convolution and obtain the elements of x * y.

${h}_{i}=\underset{k=0}{\overset{N-1}{\sum }}{x}_{k}\cdot {y}_{i-k}$

for i = 0, 1, 2, ... , M+N-2

where

• h is x * y
• N is the number of elements in x
• M is the number of elements in y
• the indexed elements outside the ranges of x and y are equal to 0, as shown in the following relationships:
${x}_{j}=0,\text{\hspace{0.17em}}j<0,\text{\hspace{0.17em}}\mathrm{or}\text{\hspace{0.17em}}j\ge N$

and

${y}_{j}=0,\text{\hspace{0.17em}}j<0,\text{\hspace{0.17em}}\mathrm{or}\text{\hspace{0.17em}}j\ge M$

Computing 2D Convolution with the Direct Method

When algorithm is direct, this node uses the following equation to compute the two-dimensional convolution of the input matrices x and y.

$h\left(i,j\right)=\underset{m=0}{\overset{{M}_{1}-1}{\sum }}\underset{n=0}{\overset{{N}_{1}-1}{\sum }}x\left(m,n\right)\cdot y\left(i-m,j-n\right)-k$

for i = 0, 1, 2, ... , M1+M2-2 and j = 0, 1, 2, ... , N1+N2-2

where

• h is x * y
• M1 is the number of rows of matrixx
• N1 is the number of columns of matrix x
• M2 is the number of rows of matrixy
• N2 is the number of columns of matrix y
• the indexed elements outside the ranges of x and y are equal to 0, as shown in the following relationships:
$x\left(m,n\right)=0,\text{\hspace{0.17em}}m<0,\text{\hspace{0.17em}}\mathrm{or}\text{\hspace{0.17em}}m\ge {M}_{1}\text{\hspace{0.17em}}\mathrm{or}\text{\hspace{0.17em}}n<0\text{\hspace{0.17em}}\mathrm{or}\text{\hspace{0.17em}}n\ge {N}_{1}$

and

$y\left(m,n\right)=0,\text{\hspace{0.17em}}m<0,\text{\hspace{0.17em}}\mathrm{or}\text{\hspace{0.17em}}m\ge {M}_{2}\text{\hspace{0.17em}}\mathrm{or}\text{\hspace{0.17em}}n<0\text{\hspace{0.17em}}\mathrm{or}\text{\hspace{0.17em}}n\ge {N}_{2}$

Default: frequency domain ## output size

Size of the convolution of the input sequences.

This input is available only if x and y are 2D arrays.

Name Description
full Sets the width of the convolution to one less than the sum of the widths of the input sequences. Sets the height of the convolution to one less than the sum of the heights of the input sequences.
size X Sets the width and height of the convolution to the width and height of the first input sequence.
compact Sets the width of the convolution to one greater than the difference of the widths of the input sequences. Sets the height of the convolution to one greater than the difference of the heights of the input sequences. The width and height of the first input sequence must be greater than or equal to the width and height of the second input sequence, respectively.

Default: full ## delay output with half y length

Delays the result of the convolution by half the length of y.

 True Delays the result of the convolution by 0.5 * N * dt where N is the number of elements in y and dt is from x. False Does not delay the result of the convolution.

This input is available when x is a waveform or an array of waveforms and y is an array of double-precision, floating-point numbers .

Default: False ## error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error  If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error ## use history data

A Boolean that specifies whether to use the data points before the current block to compute the convolution.

 True Uses the data points before the current block to compute the convolution. False Does not use the data points before the current block to compute the convolution.

This input is available only if one of the input sequences is a double-precision, floating-point number.

Default: True ## x * y

The convolution of the two input sequences.

This output can return the following data types:

• Waveform
• 1D array of waveforms
• 1D array of double-precision, floating-point numbers
• 1D array of complex double-precision, floating-point numbers
• 2D array of double-precision, floating-point numbers
• 2D array of complex double-precision, floating-point numbers ## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error  If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## Algorithm for Calculating the 1D Convolution

The linear convolution of the signals x(t) and y(t) is defined as:

$h\left(t\right)=x\left(t\right)*y\left(t\right)={\int }_{-\infty }^{\infty }x\left(\tau \right)\cdot y\left(t-\tau \right)d\tau$

where the symbol * denotes linear convolution.

This node computes the linear convolution, not the circular convolution. However, because $x\left(t\right)*{y\left(t\right)}_{N}⇔X\left(f\right)Y\left(f\right)$ is a Fourier transform pair, where $x\left(t\right)*{y\left(t\right)}_{N}$ is the circular convolution of x(t) and y(t), you can create a circular version of the convolution.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

Web Server: Not supported in VIs that run in a web application