#### FFT Bluestein

a
J
A
```package com.thealgorithms.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>
* 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++) {
}

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;
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));
}
}
}
}
```