Detecting the fundamental frequency [closed]

There's this tech-festival in IIT-Bombay, India, where they're having an event called "Artbots" where we're supposed to design artbots with artistic abilities. I had an idea about a musical robot which takes a song as input, detects the notes in the song and plays it back on a piano. I need some method which will help me compute the pitches of the notes of the song. Any idea/suggestion on how to go about it?

This is exactly what I'm doing here as my last year project :) except one thing that my project is about tracking the pitch of human singing voice (and I don't have the robot to play the tune)

The quickest way I can think of is to utilize BASS library. It contains ready-to-use function that can give you FFT data from default recording device. Take a look at "livespec" code example that comes with BASS.

By the way, raw FFT data will not enough to determine fundamental frequency. You need algorithm such as Harmonic Product Spectrum to get the F0.

Another consideration is the audio source. If you are going to do FFT and apply Harmonic Product Spectrum on it. You will need to make sure the input has only one audio source. If it contains multiple sources such as in modern songs there will be to many frequencies to consider.

Harmonic Product Spectrum Theory

If the input signal is a musical note, then its spectrum should consist of a series of peaks, corresponding to fundamental frequency with harmonic components at integer multiples of the fundamental frequency. Hence when we compress the spectrum a number of times (downsampling), and compare it with the original spectrum, we can see that the strongest harmonic peaks line up. The first peak in the original spectrum coincides with the second peak in the spectrum compressed by a factor of two, which coincides with the third peak in the spectrum compressed by a factor of three. Hence, when the various spectrums are multiplied together, the result will form clear peak at the fundamental frequency.

Method

First, we divide the input signal into segments by applying a Hanning window, where the window size and hop size are given as an input. For each window, we utilize the Short-Time Fourier Transform to convert the input signal from the time domain to the frequency domain. Once the input is in the frequency domain, we apply the Harmonic Product Spectrum technique to each window.

The HPS involves two steps: downsampling and multiplication. To downsample, we compressed the spectrum twice in each window by resampling: the first time, we compress the original spectrum by two and the second time, by three. Once this is completed, we multiply the three spectra together and find the frequency that corresponds to the peak (maximum value). This particular frequency represents the fundamental frequency of that particular window.

Limitations of the HPS method

Some nice features of this method include: it is computationally inexpensive, reasonably resistant to additive and multiplicative noise, and adjustable to different kind of inputs. For instance, we could change the number of compressed spectra to use, and we could replace the spectral multiplication with a spectral addition. However, since human pitch perception is basically logarithmic, this means that low pitches may be tracked less accurately than high pitches.

Another severe shortfall of the HPS method is that it its resolution is only as good as the length of the FFT used to calculate the spectrum. If we perform a short and fast FFT, we are limited in the number of discrete frequencies we can consider. In order to gain a higher resolution in our output (and therefore see less graininess in our pitch output), we need to take a longer FFT which requires more time.

from: http://cnx.org/content/m11714/latest/

Just a comment: The fundamental harmonic may as well be missing from a (harmonic) sound, this doesn't change the perceived pitch. As a limit case, if you take a square wave (say, a C# note) and completely suppress the first harmonic, the perceived note is still C#, in the same octave. In a way, our brain is able to compensate the absence of some harmonics, even the first, when it guesses a note. Hence, to detect a pitch with frequency-domain techniques you should take into account all the harmonics (local maxima in the magnitude of the Fourier transform), and extract some sort of "greatest common divisor" of their frequencies. Pitch detection is not a trivial problem at all...

DAFX has about 30 pages dedicated to pitch detection, with examples and Matlab code.

Autocorrelation - http://en.wikipedia.org/wiki/Autocorrelation

Zero-crossing - http://en.wikipedia.org/wiki/Zero_crossing (this method is used in cheap guitar tuners)

hahh

Try YAAPT pitch tracking, which detects fundamental frequency in both time and frequency domains. You can download Matlab source code from the link and look for peaks in the FFT output using the spectral process part.

Python package http://bjbschmitt.github.io/AMFM_decompy/pYAAPT.html#

Did you try Wikipedia's article on pitch detection? It contains a few references that can be interesting to you.

In addition, here's a list of DSP applications and libraries, where you can poke around. The list only mentions Linux software packages, but many of them are cross-platform, and there's a lot of source code you can look at.

Just FYI, detecting the pitch of the notes in a monophonic recording is within reach of most DSP-savvy people. Detecting the pitches of all notes, including chords and stuff, is a lot harder.

Rob Watson

Just a thought - but do you need to process a digital audio stream as input?

If not, consider using a symbolic representation of music (such as MIDI). The pitches of the notes will then be stated explicitly, and you can synthesize sounds (and movements) corresponding to the pitch, rhythm and many other musical parameters extremely easily.

If you need to analyse a digital audio stream (mp3, wav, live input, etc) bear in mind that while pitch detection of simple monophonic sounds is quite advanced, polyphonic pitch detection is an unsolved problem. In this case, you may find my answer to this question helpful.

For extracting the fundamental frequency of the melody from polyphonic music you could try the MELODIA plug-in: http://mtg.upf.edu/technologies/melodia

Extracting the F0's of all the instruments in a song (multi-F0 tracking) or transcribing them into notes is an even harder task. Both melody extraction and music transcription are still open research problems, so regardless of the algorithm/tool you use don't expect to obtain perfect results for either.

If you're trying to detect the notes of a polyphonic recording (multiple notes at the same time) good luck. That's a very tricky problem. I don't know of any way to listen to, say, a recording of a string quartet and have an algorithm separate the four voices. (Wavelets maybe?) If it's just one note at a time, there are several pitch tracking algorithms out there, many of them mentioned in other comments.

The algorithm you want to use will depend on the type of music you are listening to. If you want it to pick up people singing there are a lot of good algorithms out there designed specifically for voice. (That's where most of the research is.) If you are trying to pick up specific instruments you'll have to be a bit more creative. Voice algorithms can be simple because the range of the human singing voice is generally limited to about 100-2000 Hz. (Speaking range is much more narrow). The fundamental frequencies on a piano, however, go from about 27 Hz. to 4200 Hz., so you're dealing with a wider range usually ignored by voice pitch detection algorithms.

The waveform of most instruments is going to be fairly complex, with lots of harmonics, so a simple approach like counting zeros or just taking the autocorrelation won't work. If you knew roughly what frequency range you were looking in you could low-pass filter and then zero count. I'd think you'd be better off though with a more complex algorithm such as the Harmonic Product Spectrum mentioned by another user, or YAAPT ("Yet Another Algorithm for Pitch Tracking"), or something similar.

One last problem: some instruments, the piano in particular, will have the problem of missing fundamentals and inharmonicity. Missing fundamentals can be dealt with by the pitch tracking algorithms...in fact they have to be since fundamentals are often cut out in electronic transmission...though you'll probably still get some octave errors. Inharmonicity however, will give you problems if somebody plays a note in the bottom octaves of the piano. Normal pitch tracking algorithms aren't designed to deal with inharmonicity because the human voice is not significantly inharmonic.

You basically need a spectrum analyzer. You might be able to to a FFT on a recording of an analog input, but much depends on the resolution of the recording.

what immediately comes to my mind: