The answer for the question is that if you calculate the fourier transforms, magnitude spectrum etc. the indices show relative frequencies which need to be calculated to their correct value.
题
I am trying to write a small Discrete Fourier Transformation in Java to find the magnitude spectrum in a clear 400 Hz Sinus Signal (1 second as pcm signed-short)
So first I calculate the DFT for the complex values:
public void berechneDFT(int abtastwerte) {
int i;
int N = abtastwerte;
ReX = new double[N/2+1];
ImX = new double[N/2+1];
TextFileOperator tfo = new TextFileOperator(file.substring(0, file.length()-4)+"_DFT.txt");
try {
tfo.openOutputStream();
tfo.writeString("ReX ImX\n");
} catch (FileNotFoundException e) {
e.printStackTrace();
}
// real-Anteil berechnen
for (i=0, ReX[i] = 0, ImX[i] = 0; i <= N/2; i++)
{
for(int n=0; n < N; n++)
{
ReX[i] += x[n] * Math.cos( (2.0 * Math.PI * n * i) / (double) N);
ImX[i] += - (x[n] * Math.sin( (2.0 * Math.PI * n * i) / (double) N));
}
tfo.writeString(ReX[i] +" "+ImX[i]+"\n");
}
x = null;
tfo.closeOutputStream(); // flush
System.out.println("Anteile berechnet.");
}
And then I try to calculate the magnitude Spectrum:
public void berechneBetragsSpektrum() {
int N = ReX.length;
TextFileOperator tfo = new TextFileOperator("betragsspektrum_400hz.txt");
try {
tfo.openOutputStream();
} catch (FileNotFoundException e) {
e.printStackTrace();
}
double powerAtFreq;
int marker = 0;
double maxPowerAtFreq = 0;
for(int i=0; i < N; i++)
{
double A1 = ReX[i] * ReX[i];
double A2 = ImX[i] * ImX[i];
powerAtFreq = Math.sqrt(A1+A2);
if(powerAtFreq > maxPowerAtFreq)
{
maxPowerAtFreq = powerAtFreq;
marker = i;
}
tfo.writeString(powerAtFreq+"\n");
}
tfo.closeOutputStream();
System.out.println("Stärkste Frequenz: "+(marker)+" Hz");
}
But for some reason I only get the result of 400 Hz in the 'marker' if I choose to check for all 16000 samples. But shouldn't I see the peak in 400 Hz also if I only choose 800 samples, because with 800 I could see 800/2 = 400 Hz as maximum frequency?
I guess some little thing must be wrong with the code, because if I choose 800 samples I get 20 Hz, for 1600 samples I get 40 Hz which is always 1/40 * sample rate.
What the hell do I miss or did wrong? The results are strange..
Note that if I do the inverse DFT with the complex values I can reconstruct the audio signal again!
解决方案