Computes the convolution of two sequences.
The convolution method to use.
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:
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:
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.
for i = 0, 1, 2, ... , M+N-2
where
and
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.
for i = 0, 1, 2, ... , M_{1}+M_{2}-2 and j = 0, 1, 2, ... , N_{1}+N_{2}-2
where
and
Default: frequency domain
Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.
Default: No error
The convolution of the two input sequences.
The linear convolution of the signals x(t) and y(t) is defined as:
where the symbol * denotes linear convolution.
This node computes the linear convolution, not the circular convolution. However, because $x\left(t\right)*{y\left(t\right)}_{N}\iff X\left(f\right)Y\left(f\right)$ 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