#### Auto Correlation

m
package com.thealgorithms.maths;

/**
* Class for linear auto-correlation of a discrete signal
*
* @author Athina-Frederiki Swinkels
* @version 2.0
*/

public class AutoCorrelation {

/**
* Discrete linear auto-correlation function.
* Input and output signals have starting index 0.
*
* @param x The discrete signal
* @return The result of the auto-correlation of signals x. The result is also a signal.
*/
public static double[] autoCorrelation(double[] x) {

/*
To find the auto-correlation of a discrete signal x, we perform cross-correlation between x signal and itself.
Here's an example:
x=[1,2,1,1]
y=[1,2,1,1]

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

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

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

i=3:       [1,2,1,1]
[1,2,1,1]        result[3]=1*1+2*2+1*1+1*1=7

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

i=5:       [1,2,1,1]
[1,2,1,1]    result[5]=1*1+1*2=3

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

result=[1,3,5,7,5,3,1]

*/

return CrossCorrelation.crossCorrelation(x, x);
}
}