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

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

@@ -0,0 +1,67 @@
+package com.thealgorithms.maths;
+
+import java.util.ArrayList;
+
+/**
+ * Class for linear convolution of two discrete signals using the convolution
+ * theorem.
+ *
+ * @author Ioannis Karavitsis
+ * @version 1.0
+ */
+public class ConvolutionFFT {
+
+    /**
+     * This method pads the signal with zeros until it reaches the new size.
+     *
+     * @param x The signal to be padded.
+     * @param newSize The new size of the signal.
+     */
+    private static void padding(ArrayList<FFT.Complex> x, int newSize) {
+        if (x.size() < newSize) {
+            int diff = newSize - x.size();
+            for (int i = 0; i < diff; i++) {
+                x.add(new FFT.Complex());
+            }
+        }
+    }
+
+    /**
+     * Discrete linear convolution function. It uses the convolution theorem for
+     * discrete signals convolved: = IDFT(DFT(a)*DFT(b)). This is true for
+     * circular convolution. In order to get the linear convolution of the two
+     * signals we first pad the two signals to have the same size equal to the
+     * convolved signal (a.size() + b.size() - 1). Then we use the FFT algorithm
+     * for faster calculations of the two DFTs and the final IDFT.
+     *
+     * <p>
+     * More info: https://en.wikipedia.org/wiki/Convolution_theorem
+     * https://ccrma.stanford.edu/~jos/ReviewFourier/FFT_Convolution.html
+     *
+     * @param a The first signal.
+     * @param b The other signal.
+     * @return The convolved signal.
+     */
+    public static ArrayList<FFT.Complex> convolutionFFT(
+            ArrayList<FFT.Complex> a, ArrayList<FFT.Complex> b) {
+        int convolvedSize = a.size() + b.size() - 1; // The size of the convolved signal
+        padding(a, convolvedSize); // Zero padding both signals
+        padding(b, convolvedSize);
+
+        /* Find the FFTs of both signals (Note that the size of the FFTs will be bigger than the convolvedSize because of the extra zero padding in FFT algorithm) */
+        FFT.fft(a, false);
+        FFT.fft(b, false);
+        ArrayList<FFT.Complex> convolved = new ArrayList<>();
+
+        for (int i = 0; i < a.size(); i++) {
+            convolved.add(a.get(i).multiply(b.get(i))); // FFT(a)*FFT(b)
+        }
+        FFT.fft(convolved, true); // IFFT
+        convolved
+                .subList(convolvedSize, convolved.size())
+                .clear(); // Remove the remaining zeros after the convolvedSize. These extra zeros came from
+        // paddingPowerOfTwo() method inside the fft() method.
+
+        return convolved;
+    }
+}