Spectral analysis using FFT, fundamental frequency derivation

Question

I need to perform spectral analysis of a simple wav file. The things I have already done :

Read file into byte array :

ByteArrayOutputStream baos = new ByteArrayOutputStream();
byte[] buffer = new byte[1024];
int bytesRead = 0;

while ((bytesRead = audioStream.read(buffer)) != -1) {
    baos.write(buffer, 0, bytesRead);
}

fileByteArray = baos.toByteArray();

Then I transform it to the real values (doubles). I've got sample values stored in double[] array.

How can I make FFT of those samples + estimate fundamental frequency?

Using JTranforms library I tried something like this :

DoubleFFT_1D fft = new DoubleFFT_1D(reader.getSpectrum().getYvalues().length);
double[] x = reader.getSpectrum().getYvalues();
double[] frequencyArray = new double[x.lenght/2];
double[] amplitudeArray = new double[x.lenght/2];
fft.realForward(x);
int i=0;
for (int j = 0; j < x.length-2; j += 2) {
    i++;
    this.frequencyArray[i] = i;
    this.amplitudeArray[i] = Math.sqrt(Math.pow(doub[j],2) + Math.pow(doub[j + 1],2));
}

Is it correct?

All suggestions are appreciated ;)

One problem is that you don't appear to be applying a suitable window function prior to the FFT. — Paul R
auto-correlation function is another way of getting fundamental frequency. — flies

mostar mostar · Accepted Answer · 2012-08-31T06:36:18

You should use autocorrelation which can be computed efficiently with FFT:

DoubleFFT_1D fft = new DoubleFFT_1D(reader.getSpectrum().getYvalues().length);
DoubleFFT_1D ifft = new DoubleFFT_1D(reader.getSpectrum().getYvalues().length);

fft.realForward(x);
for (int i = 0; i < x.length/2; i++) {
    x[2*i] = Math.sqrt(Math.pow(x[2*i],2) + Math.pow(x[2*i+1],2));
    x[2*i+1] = 0;
}
ifft.realInverse(x);
for (int i = 1; i < x.length; i++)
    x[i] /= x[0];
x[0] = 1.0;

This code gives you a list of values for which:

x[i]: corelation with i shifts

So, for example if you have a high value (close to 1) for x[n], that means you have a fundemental signal period that is: n*(1000/sampleRateHz) msecs. This is equivalent to a frequency of: sampleRateHz/(1000*n)

Spectral analysis using FFT, fundamental frequency derivation

2 Answers