JavaAlgorithms/Maths/FFTBluestein.java

package Maths;

import java.util.ArrayList;

/**
 * Class for calculating the Fast Fourier Transform (FFT) of a discrete signal using the Bluestein's
 * algorithm.
 *
 * @author Ioannis Karavitsis
 * @version 1.0
 */
public class FFTBluestein {
  /**
   * Bluestein's FFT Algorithm.
   *
   * <p>More info: https://en.wikipedia.org/wiki/Chirp_Z-transform#Bluestein.27s_algorithm
   * http://tka4.org/materials/lib/Articles-Books/Numerical%20Algorithms/Hartley_Trasform/Bluestein%27s%20FFT%20algorithm%20-%20Wikipedia,%20the%20free%20encyclopedia.htm
   *
   * @param x The discrete signal which is then converted to the FFT or the IFFT of signal x.
   * @param inverse True if you want to find the inverse FFT.
   */
  public static void fftBluestein(ArrayList<FFT.Complex> x, boolean inverse) {
    int N = x.size();
    int bnSize = 2 * N - 1;
    int direction = inverse ? -1 : 1;
    ArrayList<FFT.Complex> an = new ArrayList<>();
    ArrayList<FFT.Complex> bn = new ArrayList<>();

    /* Initialization of the b(n) sequence (see Wikipedia's article above for the symbols used)*/
    for (int i = 0; i < bnSize; i++) bn.add(new FFT.Complex());

    for (int i = 0; i < N; i++) {
      double angle = (i - N + 1) * (i - N + 1) * Math.PI / N * direction;
      bn.set(i, new FFT.Complex(Math.cos(angle), Math.sin(angle)));
      bn.set(bnSize - i - 1, new FFT.Complex(Math.cos(angle), Math.sin(angle)));
    }

    /* Initialization of the a(n) sequence */
    for (int i = 0; i < N; i++) {
      double angle = -i * i * Math.PI / N * direction;
      an.add(x.get(i).multiply(new FFT.Complex(Math.cos(angle), Math.sin(angle))));
    }

    ArrayList<FFT.Complex> convolution = ConvolutionFFT.convolutionFFT(an, bn);

    /* The final multiplication of the convolution with the b*(k) factor  */
    for (int i = 0; i < N; i++) {
      double angle = -1 * i * i * Math.PI / N * direction;
      FFT.Complex bk = new FFT.Complex(Math.cos(angle), Math.sin(angle));
      x.set(i, bk.multiply(convolution.get(i + N - 1)));
    }

    /* Divide by N if we want the inverse FFT */
    if (inverse) {
      for (int i = 0; i < N; i++) {
        FFT.Complex z = x.get(i);
        x.set(i, z.divide(N));
      }
    }
  }
}