```
package Maths;
/**
* Class for linear convolution of two discrete signals
*
* @author Ioannis Karavitsis
* @version 1.0
*/
public class Convolution {
/**
* Discrete linear convolution function. Both input signals and the output signal must start from
* 0. If you have a signal that has values before 0 then shift it to start from 0.
*
* @param A The first discrete signal
* @param B The second discrete signal
* @return The convolved signal
*/
public static double[] convolution(double[] A, double[] B) {
double[] convolved = new double[A.length + B.length - 1];
/*
The discrete convolution of two signals A and B is defined as:
A.length
C[i] = Σ (A[k]*B[i-k])
k=0
It's obvious that: 0 <= k <= A.length , 0 <= i <= A.length + B.length - 2 and 0 <= i-k <= B.length - 1
From the last inequality we get that: i - B.length + 1 <= k <= i and thus we get the conditions below.
*/
for (int i = 0; i < convolved.length; i++) {
convolved[i] = 0;
int k = Math.max(i - B.length + 1, 0);
while (k < i + 1 && k < A.length) {
convolved[i] += A[k] * B[i - k];
k++;
}
}
return convolved;
}
}
```

A

J