62 lines
2.2 KiB
Java
62 lines
2.2 KiB
Java
package com.maths;
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import java.util.ArrayList;
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/**
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* Class for calculating the Fast Fourier Transform (FFT) of a discrete signal using the Bluestein's
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* algorithm.
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*
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* @author Ioannis Karavitsis
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* @version 1.0
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*/
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public class FFTBluestein {
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/**
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* Bluestein's FFT Algorithm.
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*
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* <p>More info: https://en.wikipedia.org/wiki/Chirp_Z-transform#Bluestein.27s_algorithm
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* http://tka4.org/materials/lib/Articles-Books/Numerical%20Algorithms/Hartley_Trasform/Bluestein%27s%20FFT%20algorithm%20-%20Wikipedia,%20the%20free%20encyclopedia.htm
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*
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* @param x The discrete signal which is then converted to the FFT or the IFFT of signal x.
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* @param inverse True if you want to find the inverse FFT.
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*/
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public static void fftBluestein(ArrayList<FFT.Complex> x, boolean inverse) {
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int N = x.size();
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int bnSize = 2 * N - 1;
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int direction = inverse ? -1 : 1;
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ArrayList<FFT.Complex> an = new ArrayList<>();
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ArrayList<FFT.Complex> bn = new ArrayList<>();
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/* Initialization of the b(n) sequence (see Wikipedia's article above for the symbols used)*/
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for (int i = 0; i < bnSize; i++) bn.add(new FFT.Complex());
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for (int i = 0; i < N; i++) {
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double angle = (i - N + 1) * (i - N + 1) * Math.PI / N * direction;
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bn.set(i, new FFT.Complex(Math.cos(angle), Math.sin(angle)));
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bn.set(bnSize - i - 1, new FFT.Complex(Math.cos(angle), Math.sin(angle)));
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}
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/* Initialization of the a(n) sequence */
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for (int i = 0; i < N; i++) {
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double angle = -i * i * Math.PI / N * direction;
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an.add(x.get(i).multiply(new FFT.Complex(Math.cos(angle), Math.sin(angle))));
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}
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ArrayList<FFT.Complex> convolution = ConvolutionFFT.convolutionFFT(an, bn);
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/* The final multiplication of the convolution with the b*(k) factor */
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for (int i = 0; i < N; i++) {
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double angle = -1 * i * i * Math.PI / N * direction;
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FFT.Complex bk = new FFT.Complex(Math.cos(angle), Math.sin(angle));
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x.set(i, bk.multiply(convolution.get(i + N - 1)));
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}
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/* Divide by N if we want the inverse FFT */
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if (inverse) {
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for (int i = 0; i < N; i++) {
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FFT.Complex z = x.get(i);
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x.set(i, z.divide(N));
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}
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}
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}
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}
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