package 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;
 }
}