angry1980.audio.utils.FFT Maven / Gradle / Ivy

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package angry1980.audio.utils;


import java.util.List;

/*************************************************************************
 * 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 {

	public static Complex[] fft(List x) {
		return fft(x.toArray(new Complex[x.size()]));
	}

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

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

		// radix 2 Cooley-Tukey FFT
		if (N % 2 != 0) {
			throw new RuntimeException("N is not a power of 2");
		}

		// fft of even terms
		Complex[] even = new Complex[N / 2];
		for (int k = 0; k < N / 2; k++) {
			even[k] = x[2 * k];
		}
		Complex[] q = fft(even);

		// fft of odd terms
		Complex[] odd = even; // reuse the array
		for (int k = 0; k < N / 2; k++) {
			odd[k] = x[2 * k + 1];
		}
		Complex[] r = fft(odd);

		// combine
		Complex[] y = new Complex[N];
		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) {
		System.out.println(title);
		System.out.println("-------------------");
		for (int i = 0; i < x.length; i++) {
			System.out.println(x[i]);
		}
		System.out.println();
	}

	/*********************************************************************
	 * Test client and sample execution
	 * 
	 * % java FFT 4 x ------------------- -0.03480425839330703
	 * 0.07910192950176387 0.7233322451735928 0.1659819820667019
	 * 
	 * y = fft(x) ------------------- 0.9336118983487516 -0.7581365035668999 +
	 * 0.08688005256493803i 0.44344407521182005 -0.7581365035668999 -
	 * 0.08688005256493803i
	 * 
	 * z = ifft(y) ------------------- -0.03480425839330703 0.07910192950176387
	 * + 2.6599344570851287E-18i 0.7233322451735928 0.1659819820667019 -
	 * 2.6599344570851287E-18i
	 * 
	 * c = cconvolve(x, x) ------------------- 0.5506798633981853
	 * 0.23461407150576394 - 4.033186818023279E-18i -0.016542951108772352
	 * 0.10288019294318276 + 4.033186818023279E-18i
	 * 
	 * d = convolve(x, x) ------------------- 0.001211336402308083 -
	 * 3.122502256758253E-17i -0.005506167987577068 - 5.058885073636224E-17i
	 * -0.044092969479563274 + 2.1934338938072244E-18i 0.10288019294318276 -
	 * 3.6147323062478115E-17i 0.5494685269958772 + 3.122502256758253E-17i
	 * 0.240120239493341 + 4.655566391833896E-17i 0.02755001837079092 -
	 * 2.1934338938072244E-18i 4.01805098805014E-17i
	 * 
	 *********************************************************************/

}