意外的結果

Question

http://jvalentino2.tripod.com/dft/index.html

我的代碼實際上只是一個以上的副本：

package it.vigtig.realtime.fourier; 

import java.io.File; 
import java.io.IOException; 

import javax.sound.sampled.AudioFormat; 
import javax.sound.sampled.AudioInputStream; 
import javax.sound.sampled.AudioSystem; 
import javax.sound.sampled.DataLine; 
import javax.sound.sampled.LineUnavailableException; 
import javax.sound.sampled.SourceDataLine; 

public class Fourier { 
    // Create a global buffer size 
    private static final int EXTERNAL_BUFFER_SIZE = 128000; 

    public static void main(String[] args) { 
     /* 
     * This code is based on the example found at: 
     * http://www.jsresources.org/examples/SimpleAudioPlayer.java.html 
     */ 

     // Get the location of the sound file 
     File soundFile = new File("res/sin440.wav"); 

     // Load the Audio Input Stream from the file 
     AudioInputStream audioInputStream = null; 
     try { 
      audioInputStream = AudioSystem.getAudioInputStream(soundFile); 
     } catch (Exception e) { 
      e.printStackTrace(); 
      System.exit(1); 
     } 

     // Get Audio Format information 
     AudioFormat audioFormat = audioInputStream.getFormat(); 

     // Handle opening the line 
     SourceDataLine line = null; 
     DataLine.Info info = new DataLine.Info(SourceDataLine.class, 
       audioFormat); 
     try { 
      line = (SourceDataLine) AudioSystem.getLine(info); 
      line.open(audioFormat); 
     } catch (LineUnavailableException e) { 
      e.printStackTrace(); 
      System.exit(1); 
     } catch (Exception e) { 
      e.printStackTrace(); 
      System.exit(1); 
     } 

     // Start playing the sound 
     line.start(); 

     // Write the sound to an array of bytes 
     int nBytesRead = 0; 
     byte[] abData = new byte[EXTERNAL_BUFFER_SIZE]; 
     while (nBytesRead != -1) { 
      try { 
       nBytesRead = audioInputStream.read(abData, 0, abData.length); 

      } catch (IOException e) { 
       e.printStackTrace(); 
      } 
      if (nBytesRead >= 0) { 
       int nBytesWritten = line.write(abData, 0, nBytesRead); 
      } 

     } 

     // close the line 
     line.drain(); 
     line.close(); 

     // Calculate the sample rate 
     float sample_rate = audioFormat.getSampleRate(); 
     System.out.println("sample rate = " + sample_rate); 

     // Calculate the length in seconds of the sample 
     float T = audioInputStream.getFrameLength() 
       /audioFormat.getFrameRate(); 
     System.out 
       .println("T = " + T + " (length of sampled sound in seconds)"); 

     // Calculate the number of equidistant points in time 
     int n = (int) (T * sample_rate)/2; 
     System.out.println("n = " + n + " (number of equidistant points)"); 

     // Calculate the time interval at each equidistant point 
     float h = (T/n); 
     System.out.println("h = " + h 
       + " (length of each time interval in seconds)"); 

     float fourierFreq = (sample_rate/((float) n/2f)); 
     System.out.println("Fourier frequency is:" + fourierFreq); 

     // Determine the original Endian encoding format 
     boolean isBigEndian = audioFormat.isBigEndian(); 

     // this array is the value of the signal at time i*h 
     int x[] = new int[n]; 

     // convert each pair of byte values from the byte array to an Endian 
     // value 
     for (int i = 0; i < n * 2; i += 2) { 
      int b1 = abData[i]; 
      int b2 = abData[i + 1]; 
      if (b1 < 0) 
       b1 += 0x100; 
      if (b2 < 0) 
       b2 += 0x100; 

      int value; 

      // Store the data based on the original Endian encoding format 
      if (!isBigEndian) 
       value = (b1 << 8) + b2; 
      else 
       value = b1 + (b2 << 8); 
      x[i/2] = value; 
     } 

     // do the DFT for each value of x sub j and store as f sub j 
     double maxAmp = 0.0; 
     double f[] = new double[n/2]; 
     for (int j = 1; j < n/2; j++) { 

      double firstSummation = 0; 
      double secondSummation = 0; 

      for (int k = 0; k < n; k++) { 
       double twoPInjk = ((2 * Math.PI)/n) * (j * k); 
       firstSummation += x[k] * Math.cos(twoPInjk); 
       secondSummation += x[k] * Math.sin(twoPInjk); 
      } 

      f[j] = Math.abs(Math.sqrt(Math.pow(firstSummation, 2) 
        + Math.pow(secondSummation, 2))); 

      double amplitude = 2 * f[j]/n; 
      double frequency = j * h/T * sample_rate; 

      if (amplitude > maxAmp) { 
       maxAmp = amplitude; 
       System.out.println("frequency = " + frequency + ", amp = " 
         + amplitude); 
      } 
     } 
     // System.out.println(maxAmp + "," + maxFreq + "," + maxIndex); 

    } 
} 

當我在這個示例運行：http://vigtig.it/sin440.wav

我得到這個結果：

sample rate = 8000.0 
T = 0.999875 (length of sampled sound in seconds) 
n = 3999 (number of equidistant points) 
h = 2.5003127E-4 (length of each time interval in seconds) 
Fourier frequency is:4.0010004 
frequency = 2.000500202178955, amp = 130.77640790523128 
frequency = 4.00100040435791, amp = 168.77080135041228 
frequency = 6.001501083374023, amp = 291.55653027302816 
frequency = 26.006502151489258, amp = 326.4618004521384 
frequency = 40.01000213623047, amp = 2265.126299970012 
frequency = 200.05003356933594, amp = 3310.905259926063 
frequency = 360.09002685546875, amp = 9452.570363111812 

我希望喜440赫茲的最高響應，但事實並非如此。有人能看到一個錯誤或啓發我如何誤解結果嗎？

編輯

通過字節/ INT轉換看後，我改變了腳本使用的ByteBuffer來代替。它現在似乎按預期工作。這裏是工作副本：

package it.vigtig.realtime.fourier; 

import java.io.File; 
import java.io.IOException; 
import java.nio.ByteBuffer; 
import java.nio.ShortBuffer; 

import javax.sound.sampled.AudioFormat; 
import javax.sound.sampled.AudioInputStream; 
import javax.sound.sampled.AudioSystem; 
import javax.sound.sampled.DataLine; 
import javax.sound.sampled.LineUnavailableException; 
import javax.sound.sampled.SourceDataLine; 

public class Fourier { 
    // Create a global buffer size 
    private static final int EXTERNAL_BUFFER_SIZE = 16000*16; 

    public static void main(String[] args) { 
     /* 
     * This code is based on the example found at: 
     * http://www.jsresources.org/examples/SimpleAudioPlayer.java.html 
     */ 

     // Get the location of the sound file 
     File soundFile = new File("res/saw880.wav"); 

     // Load the Audio Input Stream from the file 
     AudioInputStream audioInputStream = null; 
     try { 
      audioInputStream = AudioSystem.getAudioInputStream(soundFile); 
     } catch (Exception e) { 
      e.printStackTrace(); 
      System.exit(1); 
     } 

     // Get Audio Format information 
     AudioFormat audioFormat = audioInputStream.getFormat(); 

     // Handle opening the line 
     SourceDataLine line = null; 
     DataLine.Info info = new DataLine.Info(SourceDataLine.class, 
       audioFormat); 
     try { 
      line = (SourceDataLine) AudioSystem.getLine(info); 
      line.open(audioFormat); 
     } catch (LineUnavailableException e) { 
      e.printStackTrace(); 
      System.exit(1); 
     } catch (Exception e) { 
      e.printStackTrace(); 
      System.exit(1); 
     } 

     // Start playing the sound 
     line.start(); 

     // Write the sound to an array of bytes 
     int nBytesRead = 0; 
     byte[] abData = new byte[EXTERNAL_BUFFER_SIZE]; 
     while (nBytesRead != -1) { 
      try { 
       nBytesRead = audioInputStream.read(abData, 0, abData.length); 

      } catch (IOException e) { 
       e.printStackTrace(); 
      } 
      if (nBytesRead >= 0) { 
       int nBytesWritten = line.write(abData, 0, nBytesRead); 
      } 

     } 

     // close the line 
     line.drain(); 
     line.close(); 

     // Calculate the sample rate 
     float sample_rate = audioFormat.getSampleRate(); 
     System.out.println("sample rate = " + sample_rate); 

     // Calculate the length in seconds of the sample 
     float T = audioInputStream.getFrameLength() 
       /audioFormat.getFrameRate(); 
     System.out 
       .println("T = " + T + " (length of sampled sound in seconds)"); 

     // Calculate the number of equidistant points in time 
     int n = (int) (T * sample_rate)/2; 
     System.out.println("n = " + n + " (number of equidistant points)"); 

     // Calculate the time interval at each equidistant point 
     float h = (T/n); 
     System.out.println("h = " + h 
       + " (length of each time interval in seconds)"); 

     float fourierFreq = (sample_rate/((float) n/2f)); 
     System.out.println("Fourier frequency is:" + fourierFreq); 

     // Determine the original Endian encoding format 
     boolean isBigEndian = audioFormat.isBigEndian(); 

     // this array is the value of the signal at time i*h 
     int x[] = new int[n]; 

     ByteBuffer bb = ByteBuffer.allocate(n * 2); 

     for (int i = 0; i < n * 2; i++) 
      bb.put(abData[i]); 


     // do the DFT for each value of x sub j and store as f sub j 
     double maxAmp = 0.0; 
     double f[] = new double[n/2]; 
     for (int j = 1; j < n/2; j++) { 

      double firstSummation = 0; 
      double secondSummation = 0; 

      for (int k = 0; k < n; k++) { 
       double twoPInjk = ((2 * Math.PI)/n) * (j * k); 
       firstSummation += bb.getShort(k) * Math.cos(twoPInjk); 
       secondSummation += bb.getShort(k) * Math.sin(twoPInjk); 
      } 

      f[j] = Math.abs(Math.sqrt(Math.pow(firstSummation, 2) 
        + Math.pow(secondSummation, 2))); 

      double amplitude = 2 * f[j]/n; 
      double frequency = j * h/T * sample_rate; 

      if (amplitude > maxAmp) { 
       maxAmp = amplitude; 
       System.out.println("frequency = " + frequency*2 + ", amp = " 
         + amplitude); 
      } 
     } 
//  System.out.println(maxAmp + "," + maxFreq + "," + maxIndex); 

    } 
} 

Answer 1

將字節對轉換爲帶符號整數似乎是錯誤的。頻率的計算似乎是錯誤的。也許長度值也不好。

如果輸入不正確，則無法解釋DFT結果。嘗試繪製DFT輸入（時域波形）並查看看起來是否合適。

Answer 2

你需要應用FFT一個window function之前，否則你將看到的spectral leakage的影響，這通常會導致振幅譜的拖尾現象。