Version:

Last Modified: January 9, 2017

Computes the two-dimensional cross correlation of two sequences.

The first input sequence.

This input can be a 2D array of double-precision, floating-point numbers or a 2D array of complex double-precision, floating-point numbers.

The second input sequence.

This input can be a 2D array of double-precision, floating-point numbers or a 2D array of complex double-precision, floating-point numbers.

The correlation 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 |
---|---|

direct | Computes the cross correlation using the direct method of linear correlation. |

frequency domain | Computes the cross correlation using an FFT-based technique. |

**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 cross correlation of the two input sequences.

This node computes two-dimensional cross correlation as follows:

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

for *i* = -(*M*_{1}-1), ..., -1, 0, 1, ... , (*M*_{2}-1) and *j* = -(*N*_{1}-1), ..., -1, 0, 1, ... , (*N*_{2}-1)

where

*M*_{1}is the number of rows of matrix**X***N*_{1}is the number of columns of matrix**X***M*_{2}is the number of rows of matrix**Y***N*_{2}is the number of columns of matrix**Y**

The indexed elements outside the ranges of **X** and **Y** are equal to zero, as shown in the following relationships:

$x(m,n)=0,\text{\hspace{0.17em}}m<0\text{\hspace{0.17em}}\mathrm{or}\text{\hspace{0.17em}}m\ge {M}_{1}\text{\hspace{0.17em}}\mathrm{or}\text{\hspace{0.17em}}n<0\text{\hspace{0.17em}}\mathrm{or}\text{\hspace{0.17em}}n\ge {N}_{1}$

and

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

The elements of the output matrix **RXY** are related to the elements in *h* as follows:

${R}_{xy}(i,j)=h(i-({M}_{1}-1),j-({N}_{1}-1))\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{for}\text{\hspace{0.17em}}i=0,\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}2,\text{\hspace{0.17em}}\mathrm{...},\text{\hspace{0.17em}}{M}_{1}+{M}_{2}-2\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{and}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}j=0,\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}2,\text{\hspace{0.17em}}\mathrm{...},\text{\hspace{0.17em}}{N}_{1}+{N}_{2}-2$

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: Not supported