xcorr2

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Two-dimensional cross-correlation function.

Library

EngeeDSP

Syntax

Function call

c = xcorr2(a,b) — returns the cross-correlation of the matrices a and b without scaling. Function xcorr2 — this is a two-dimensional version of the function xcorr.

c = xcorr2(a) — the autocorrelation matrix of the input matrix a. This syntax is equivalent to xcorr2(a,a).

Arguments

Input arguments

# a — input array

+ the matrix

Details

The input array, specified as a matrix.

Data types	`Float32`, `Float64`
Support for complex numbers	Yes

# b — input array

+ the matrix

Details

The input array specified as a matrix.

Data types	`Float32`, `Float64`
Support for complex numbers	Yes

Output arguments

# c is a two- dimensional cross-correlation or autocorrelation matrix

+ the matrix

Details

A two-dimensional cross-correlation or autocorrelation matrix returned as a matrix.

Additional Info

Two-dimensional cross-correlation

Two-dimensional cross-correlation of the matrix size on and matrices size on It represents a matrix size on . Its elements are given by the formula

Where the hell is means complex conjugation.

The output matrix It has negative and positive row and column indexes.

A negative row index corresponds to a shift in the rows of the matrix up.
A negative column index corresponds to a shift in the columns of the matrix to the left.
A positive row index corresponds to a shift in the rows of the matrix down.
A positive column index corresponds to a shift in the columns of the matrix to the right.

To convert the indexes to the Engee form, add the size of the matrix — element corresponds to the element C(k+P,l+Q) in the workspace.

For example, consider the following two-dimensional cross-correlation:

X = ones(2,3);
H = [1 2; 3 4; 5 6];  # H is 3 by 2
C = xcorr2(X,H)

C =
     6    11    11     5
    10    18    18     8
     6    10    10     4
     2     3     3     1

Element C(1,1) the output data corresponds to in a characteristic equation that uses indexing from scratch. To calculate an element C(1,1), move it H two rows up and one column to the left. Accordingly, the only product in the sum of the cross-correlation will be X(1,1)*H(3,2)=6. Using the characteristic equation, we obtain

in this case, all other terms of the double sum are equal to zero.