#### Convolution FFT

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```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++) {
}
}
}

/**
* 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>
* 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

/* 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++) {
}
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;
}
}
```  