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. * *

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 x, boolean inverse) { int N = x.size(); int bnSize = 2 * N - 1; int direction = inverse ? -1 : 1; ArrayList an = new ArrayList<>(); ArrayList 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 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)); } } } }