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;
 }
}