#### Cross Correlation

m
```package com.thealgorithms.maths;

/**
* Class for linear cross-correlation of two discrete signals
*
* @author Athina-Frederiki Swinkels
* @version 1.0
*/

public class CrossCorrelation {

/**
* Discrete linear cross-correlation function.
* Input and output signals have starting index 0.
*
* @param x The first discrete signal
* @param y The second discrete signal
* @return The result of the cross-correlation of signals x,y. The result is also a signal.
*/
public static double[] crossCorrelation(double[] x, double[] y) {
// The result signal's length is the sum of the input signals' lengths minus 1
double[] result = new double[x.length + y.length - 1];
int N = result.length;

/*
To find the cross-correlation between 2 discrete signals x & y, we start by "placing" the second signal
y under the first signal x, shifted to the left so that the last value of y meets the first value of x
and for every new position (i++) of the result signal, we shift y signal one position to the right, until
the first y-value meets the last x-value. The result-value for each position is the sum of all x*y meeting
values.
Here's an example:
x=[1,2,1,1]
y=[1,1,2,1]

i=0:      [1,2,1,1]
[1,1,2,1]               result[0]=1*1=1

i=1:       [1,2,1,1]
[1,1,2,1]            result[1]=1*2+2*1=4

i=2:       [1,2,1,1]
[1,1,2,1]          result[2]=1*1+2*2+1*1=6

i=3:       [1,2,1,1]
[1,1,2,1]        result[3]=1*1+2*1+1*2+1*1=6

i=4:       [1,2,1,1]
[1,1,2,1]      result[4]=2*1+1*1+1*2=5

i=5:       [1,2,1,1]
[1,1,2,1]    result[5]=1*1+1*1=2

i=1:       [1,2,1,1]
[1,1,2,1]  result[6]=1*1=1

result=[1,4,6,6,5,2,1]

To find the result[i] value for each i:0->N-1, the positions of x-signal in which the 2 signals meet
are calculated: kMin<=k<=kMax.
The variable 'yStart' indicates the starting index of y in each sum calculation.
The variable 'count' increases the index of y-signal by 1, to move to the next value.
*/
int yStart = y.length;
for (int i = 0; i < N; i++) {
result[i] = 0;

int kMin = Math.max(i - (y.length - 1), 0);
int kMax = Math.min(i, x.length - 1);

if (i < y.length) {
yStart--;
}

int count = 0;
for (int k = kMin; k <= kMax; k++) {
result[i] += x[k] * y[yStart + count];
count++;
}
}

// The calculated cross-correlation of x & y signals is returned here.
return result;
}
}
```