# Harmonic Product Spectrum limitations in pitch detection

I've made a pitch detection algorithm using HPS and I'm facing a problem. I'm a beginner with signal processing and this site helped me before, so I though I should ask.

For higher pitches ( eg. >C6:1046.50hz ) I'm starting to get garbage data from the HPS. The higher the pitch the more garbage I get (by garbage I mean frequencies that are not octave errors nor harmonics and are around 1Hz-20Hz)

What I've empirical observed:

1. the results are worst for higher pitches, if the fundamental is above A6 or so, I get only garbage data.

2. the FFT works fine even for a very high pitch, (by fine I mean that its peak shows either the fundamental or one of its harmonics, but not garbage)

3. if I lower the number of harmonics I take in consideration for the HPS, the garbage diminishes, but that makes it harder to discriminate between the fundamental and the harmonics.

Here is my algorithm:

->raw buffer -> hann window, 16384 samples, 50% overlap -> zero padding -> FFT -> HPS

Any help is appreciated!

UPDATE 1: So, there are a few more things I want to add:

1. The sample rate I'm recording at is 44100 Hz
2. I've observed that this behavior is barely visible on a guitar, but very visible on an digital piano (for the same played note)
3. Here is my hps algorithm, maybe someone with greater experience can spot a problem.

int hps(float* spectrum, int spectrumSize, int harmonics) {

int i, j, maxSearchIndex, maxBin;
maxSearchIndex = spectrumSize/harmonics;

maxBin = 1;
for (j=1; j<=maxSearchIndex; j++) {
for (i=1; i<=harmonics; i++) {
spectrum[j] *= spectrum[j*i];
}
if (spectrum[j] > spectrum[maxBin]) {
maxBin = j;
}
}

// Fixing octave too high errors
int correctMaxBin = 1;
int maxsearch = maxBin * 3 / 4;
for (i=2; i<maxsearch; i++) {
if (spectrum[i] > spectrum[correctMaxBin]) {
correctMaxBin = i;
}
}
if (abs(correctMaxBin * 2 - maxBin) < 4) {
if (spectrum[correctMaxBin]/spectrum[maxBin] > 0.2) {
maxBin = correctMaxBin;
}
}

return maxBin;
}

• What's your sample rate? What anti-aliasing filter have you got before the ADC? – Martin Thompson Nov 3 '11 at 13:03
• My recording sample rate is 44100 Hz, sorry I didn't mention it before. – Valentin Radu Nov 3 '11 at 13:28
• 1. You need to plot the intermediate spectra and products used in the HPS calculation and see where it's getting the wrong values from. 2. Guitar and piano are inharmonic, which will cause the peaks to not line up perfectly. Not sure how much of an effect this would have, but HPS assumes perfectly harmonic spectra. – endolith Aug 27 '12 at 14:51