予期しない結果が

Question

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

私のコードは、実際に上記の単なるコピーである：http://vigtig.it/sin440.wav

：私はこのサンプルで実行

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); 

    } 
} 

この結果が得られます：

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 

440 hzで応答を得たが、これはそうではない。誰かがバグを見たり、私が結果をどうやって誤解しているかについて教えてもらえますか？

EDIT

バイト/ int型の変換を見た後、私が代わりのByteBufferを使用するようにスクリプトを変更しました。今のところ意図どおりに動作するようです。そうでなければ、一般的に振幅スペクトルの不鮮明になりspectral leakageの効果を、表示されます、

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

バイトペアの符号付き整数への変換が間違っているようです。頻度の計算は間違っているようです。おそらく長さの値も悪いです。

入力が不良の場合、DFT結果を解釈できません。 DFT入力（時間領域波形）をプロットして、それが最初に適切かどうかを確認してください。

Answer 2

あなたはwindow function FFT前に適用する必要があります。ここでは作業コピーです。