``````package Maths;

import java.util.ArrayList;

/**
* Class for circular convolution of two discrete signals using the convolution theorem.
*
* @author Ioannis Karavitsis
* @version 1.0
*/
public class CircularConvolutionFFT {
/**
* 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 circular convolution function. It uses the convolution theorem for discrete signals:
* convolved = IDFT(DFT(a)*DFT(b)). Then we use the FFT algorithm for faster calculations of the
* two DFTs and the final IDFT.
*
*
* @param a The first signal.
* @param b The other signal.
* @return The convolved signal.
*/
public static ArrayList<FFT.Complex> fftCircularConvolution(
ArrayList<FFT.Complex> a, ArrayList<FFT.Complex> b) {
int convolvedSize =
Math.max(
a.size(), b.size()); // The two signals must have the same size equal to the bigger one

/* Find the FFTs of both signal. Here we use the Bluestein algorithm because we want the FFT to have the same length with the signal and not bigger */
FFTBluestein.fftBluestein(a, false);
FFTBluestein.fftBluestein(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)

FFTBluestein.fftBluestein(convolved, true); // IFFT

return convolved;
}
}
``````

#### CircularConvolutionFFT

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