FFT.java

package org.mobicents.media.server.impl.resource.fft;

import org.apache.log4j.Logger;

/*******************************************************************************
 * Compilation: javac FFT.java Execution: java FFT N Dependencies: Complex.java
 * 
 * Compute the FFT and inverse FFT of a length N complex sequence. Bare bones
 * implementation that runs in O(N log N) time. Our goal is to optimize the
 * clarity of the code, rather than performance.
 * 
 * Limitations ----------- - assumes N is a power of 2 - not the most memory
 * efficient algorithm (because it uses an object type for representing complex
 * numbers and because it re-allocates memory for the subarray, instead of doing
 * in-place or reusing a single temporary array)
 * 
 ******************************************************************************/

public class FFT {
	
	private static Logger logger = Logger.getLogger(FFT.class);

	// compute the FFT of x[], assuming its length is a power of 2
	public Complex[] fft(Complex[] x) {
		int N = x.length;
		Complex[] y = new Complex[N];

		// base case
		if (N == 1) {
			y[0] = x[0];
			return y;
		}

		// radix 2 Cooley-Tukey FFT
		if (N % 2 != 0)
			throw new RuntimeException("N is not a power of 2");
		Complex[] even = new Complex[N / 2];
		Complex[] odd = new Complex[N / 2];
		for (int k = 0; k < N / 2; k++)
			even[k] = x[2 * k];
		for (int k = 0; k < N / 2; k++)
			odd[k] = x[2 * k + 1];

		Complex[] q = fft(even);
		Complex[] r = fft(odd);

		for (int k = 0; k < N / 2; k++) {
			double kth = -2 * k * Math.PI / N;
			Complex wk = new Complex(Math.cos(kth), Math.sin(kth));
			y[k] = q[k].plus(wk.times(r[k]));
			y[k + N / 2] = q[k].minus(wk.times(r[k]));
		}
		return y;
	}

	// compute the inverse FFT of x[], assuming its length is a power of 2
	/*
	 * public static Complex[] ifft(Complex[] x) { int N = x.length; Complex[] y =
	 * new Complex[N]; // take conjugate for (int i = 0; i < N; i++) { y[i] =
	 * x[i].conjugate(); } // compute forward FFT y = fft(y); // take conjugate
	 * again for (int i = 0; i < N; i++) { y[i] = y[i].conjugate(); } // divide
	 * by N for (int i = 0; i < N; i++) { y[i] = y[i].times(1.0 / N); }
	 * 
	 * return y; } // compute the circular convolution of x and y public static
	 * Complex[] cconvolve(Complex[] x, Complex[] y) { // should probably pad x
	 * and y with 0s so that they have same length // and are powers of 2 if
	 * (x.length != y.length) { throw new RuntimeException("Dimensions don't
	 * agree"); }
	 * 
	 * int N = x.length; // compute FFT of each sequence Complex[] a = fft(x);
	 * Complex[] b = fft(y); // point-wise multiply Complex[] c = new
	 * Complex[N]; for (int i = 0; i < N; i++) { c[i] = a[i].times(b[i]); } //
	 * compute inverse FFT return ifft(c); } // compute the linear convolution
	 * of x and y public static Complex[] convolve(Complex[] x, Complex[] y) {
	 * Complex ZERO = new Complex(0, 0);
	 * 
	 * Complex[] a = new Complex[2 * x.length]; for (int i = 0; i < x.length;
	 * i++) a[i] = x[i]; for (int i = x.length; i < 2 * x.length; i++) a[i] =
	 * ZERO;
	 * 
	 * Complex[] b = new Complex[2 * y.length]; for (int i = 0; i < y.length;
	 * i++) b[i] = y[i]; for (int i = y.length; i < 2 * y.length; i++) b[i] =
	 * ZERO;
	 * 
	 * return cconvolve(a, b); } // display an array of Complex numbers to
	 * standard output
	 * 
	 */

	public static void show(Complex[] x, String title) {
		logger.debug(title);
		logger.debug("-------------------");
		for (int i = 0; i < x.length; i++) {
			logger.debug(x[i]);
		}
		logger.debug("");
	}

}