Change project structure to a Maven Java project + Refactor (#2816)

src/main/java/com/thealgorithms/maths/Convolution.java

@@ -0,0 +1,45 @@
+package com.thealgorithms.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;
+    }
+}