JavaAlgorithms/Maths/Convolution.java

package com.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;
  }
}