FFT.java

/*********************************************
 * ANDROID SOUND PRESSURE METER APPLICATION	  * ANDROID SOUND PRESSURE METER APPLICATION
  * DESC   : FFT File. Taken from  	  * DESC   : FFT File. Taken from  
  * WEBSRC : http://www.cs.princeton.edu/introcs/97data/FFT.java.html	 
- * AUTHOR : hashir.mail@gmail.com	
- * DATE   : 19 JUNE 2009	
  * CHANGES: Commented the main method.	  * CHANGES: Commented the main method.
  * UNTESTED 
  *********************************************/

package android.ilus.spltest.android.ilus;

public class FFT
{

    // 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
     * 
     *********************************************************************/
    /*
     * public static void main(String[] args) { int N =
     * Integer.parseInt(args[0]); Complex[] x = new Complex[N];
     * 
     * // original data for (int i = 0; i < N; i++) { x[i] = new Complex(i, 0);
     * // x[i] = new Complex(-2*Math.random() + 1, 0); } show(x, "x");
     * 
     * // FFT of original data Complex[] y = fft(x); show(y, "y = fft(x)");
     * 
     * // take inverse FFT Complex[] z = ifft(y); show(z, "z = ifft(y)");
     * 
     * // circular convolution of x with itself Complex[] c = cconvolve(x, x);
     * show(c, "c = cconvolve(x, x)");
     * 
     * // linear convolution of x with itself Complex[] d = convolve(x, x);
     * show(d, "d = convolve(x, x)"); }
     */
}