Harmonic Product Spectrum from FFT output to the fundamental frequency

Question

I'm trying to do the HPS algorithm on my FFT output, but I'm stuck here. My signal is from a bass (cable), 16bits, 48.000Hz.

I split in time domain the array of the whole record into multiple arrays of 24.000 frames (miniBuffer[24000]).

I'm applying a Hamming window once it's split, like this:

miniBuffer [m] = miniBuffer [m] * 0.5 * (1.0 - Math.cos(2.0*Math.PI*m/24000));

Then, I compute FFT on each array.

Finally I try the HPS:

 double mag[] = new double[miniBuffer.length]; //Saves magnitude of the fft values

 double m_max0 = miniBuffer[0];

                    for (int i=0; i < miniBuffer.length / 2 - 1; i++) {
                        double real = miniBuffer[2*i];
                        double imag = miniBuffer[2*i+1];
                        //Gets magnitude
                        mag[i] = (float)Math.sqrt(real*real + imag * imag);

                        if (miniBuffer[i] > m_max0 && i>0) {
                         m_max0 = miniBuffer[i];
                        }
                    }


                 int i_max = 0;
                 double m_max = miniBuffer[0]; //max
                 m_max = m_max0;

                 double sum [] = new double[miniBuffer.length];
                 int fund_freq = 0;

                 //HPS

                 for(int k = 0; k < 24000/48 ; k++)
                 {
                     sum[k] = miniBuffer[k] * miniBuffer[2*k] * miniBuffer[3*k];
                     // find fundamental frequency (maximum value in plot)
                     if( sum[k] > m_max && k > 0 )
                     {
                         m_max = sum[k];
                         i_max = k;
                     }
                  }
                  fund_freq = i_max * 48000 / 24000;
                  System.out.println(fund_freq);

The values of the max magnitude are the frequency that is recording the program, but when i apply the HPS, for example, to a 220Hz sound, the HPS returns me 26 or 30.

I think that this values come from the frequencies limiter that doesn't works (I want to cap before 37Hz and after 440):

                 double hz = ((double)( miniBuffer.length * 2)) /48000;

                 for(int z = 0; z<(37*hz); z++) {
                     miniBuffer[z] = Double.NEGATIVE_INFINITY;
                 }
                 for(int z = 0; z>(440*hz); z++) {
                     miniBuffer[z] = Double.NEGATIVE_INFINITY;
                 }

If I delete this, HPS returns me 0 in every output.

So:

• Is the window correctly applied?
• Is the HPS a good algorithm for bass pitch detection? (Low Frequency)
• What could i use for limit my values in a right way?
• How to fix my HPS algorithm?
• Some other advice?

Thank you!

Answer 1

If you zero out most or all of the harmonics (you set them all to -inf in your cap), then the HPS algorithm can’t find them.