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FFT.java

/*
 *  Copyright 2006-2007 Columbia University.
 *
 *  This file is part of MEAPsoft.
 *
 *  MEAPsoft is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License version 2 as
 *  published by the Free Software Foundation.
 *
 *  MEAPsoft is distributed in the hope that it will be useful, but
 *  WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 *  General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with MEAPsoft; if not, write to the Free Software
 *  Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA
 *  02110-1301 USA
 *
 *  See the file "COPYING" for the text of the license.
 */

package com.meapsoft;


public class FFT {

  int n, m;
  
  // Lookup tables.  Only need to recompute when size of FFT changes.
  double[] cos;
  double[] sin;

  double[] window;
  
  public FFT(int n) {
    this.n = n;
    this.m = (int)(Math.log(n) / Math.log(2));

    // Make sure n is a power of 2
    if(n != (1<<m))
      throw new RuntimeException("FFT length must be power of 2");

    // precompute tables
    cos = new double[n/2];
    sin = new double[n/2];

//     for(int i=0; i<n/4; i++) {
//       cos[i] = Math.cos(-2*Math.PI*i/n);
//       sin[n/4-i] = cos[i];
//       cos[n/2-i] = -cos[i];
//       sin[n/4+i] = cos[i];
//       cos[n/2+i] = -cos[i];
//       sin[n*3/4-i] = -cos[i];
//       cos[n-i]   = cos[i];
//       sin[n*3/4+i] = -cos[i];        
//     }

    for(int i=0; i<n/2; i++) {
      cos[i] = Math.cos(-2*Math.PI*i/n);
      sin[i] = Math.sin(-2*Math.PI*i/n);
    }

    makeWindow();
  }

  protected void makeWindow() {
    // Make a blackman window:
    // w(n)=0.42-0.5cos{(2*PI*n)/(N-1)}+0.08cos{(4*PI*n)/(N-1)};
    window = new double[n];
    for(int i = 0; i < window.length; i++)
      window[i] = 0.42 - 0.5 * Math.cos(2*Math.PI*i/(n-1)) 
        + 0.08 * Math.cos(4*Math.PI*i/(n-1));
  }
  
  public double[] getWindow() {
    return window;
  }


  /***************************************************************
  * fft.c
  * Douglas L. Jones 
  * University of Illinois at Urbana-Champaign 
  * January 19, 1992 
  * http://cnx.rice.edu/content/m12016/latest/
  * 
  *   fft: in-place radix-2 DIT DFT of a complex input 
  * 
  *   input: 
  * n: length of FFT: must be a power of two 
  * m: n = 2**m 
  *   input/output 
  * x: double array of length n with real part of data 
  * y: double array of length n with imag part of data 
  * 
  *   Permission to copy and use this program is granted 
  *   as long as this header is included. 
  ****************************************************************/
  public void fft(double[] x, double[] y)
  {
    int i,j,k,n1,n2,a;
    double c,s,e,t1,t2;
  
  
    // Bit-reverse
    j = 0;
    n2 = n/2;
    for (i=1; i < n - 1; i++) {
      n1 = n2;
      while ( j >= n1 ) {
        j = j - n1;
        n1 = n1/2;
      }
      j = j + n1;
    
      if (i < j) {
        t1 = x[i];
        x[i] = x[j];
        x[j] = t1;
        t1 = y[i];
        y[i] = y[j];
        y[j] = t1;
      }
    }

    // FFT
    n1 = 0;
    n2 = 1;
  
    for (i=0; i < m; i++) {
      n1 = n2;
      n2 = n2 + n2;
      a = 0;
    
      for (j=0; j < n1; j++) {
        c = cos[a];
        s = sin[a];
        a +=  1 << (m-i-1);

        for (k=j; k < n; k=k+n2) {
          t1 = c*x[k+n1] - s*y[k+n1];
          t2 = s*x[k+n1] + c*y[k+n1];
          x[k+n1] = x[k] - t1;
          y[k+n1] = y[k] - t2;
          x[k] = x[k] + t1;
          y[k] = y[k] + t2;
        }
      }
    }
  }                          




  // Test the FFT to make sure it's working
  public static void main(String[] args) {
    int N = 8;

    FFT fft = new FFT(N);

    double[] window = fft.getWindow();
    double[] re = new double[N];
    double[] im = new double[N];

    // Impulse
    re[0] = 1; im[0] = 0;
    for(int i=1; i<N; i++)
      re[i] = im[i] = 0;
    beforeAfter(fft, re, im);

    // Nyquist
    for(int i=0; i<N; i++) {
      re[i] = Math.pow(-1, i);
      im[i] = 0;
    }
    beforeAfter(fft, re, im);

    // Single sin
    for(int i=0; i<N; i++) {
      re[i] = Math.cos(2*Math.PI*i / N);
      im[i] = 0;
    }
    beforeAfter(fft, re, im);

    // Ramp
    for(int i=0; i<N; i++) {
      re[i] = i;
      im[i] = 0;
    }
    beforeAfter(fft, re, im);

    long time = System.currentTimeMillis();
    double iter = 30000;
    for(int i=0; i<iter; i++)
      fft.fft(re,im);
    time = System.currentTimeMillis() - time;
    System.out.println("Averaged " + (time/iter) + "ms per iteration");
  }

  protected static void beforeAfter(FFT fft, double[] re, double[] im) {
    System.out.println("Before: ");
    printReIm(re, im);
    fft.fft(re, im);
    System.out.println("After: ");
    printReIm(re, im);
  }

  protected static void printReIm(double[] re, double[] im) {
    System.out.print("Re: [");
    for(int i=0; i<re.length; i++)
      System.out.print(((int)(re[i]*1000)/1000.0) + " ");

    System.out.print("]\nIm: [");
    for(int i=0; i<im.length; i++)
      System.out.print(((int)(im[i]*1000)/1000.0) + " ");

    System.out.println("]");
  }
}

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