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;

}

}