Real-time (~10ms latency) pitch detection of monophonic signals, presented as a single-file C header library (for ease of use; inspired by the stb libraries).
It's based on the MPM algorithm from "A Smarter Way to Find Pitch" by McLeod and Wyvill, but it uses spectrogram analysis to further refine the result.
The MPM algorithm produces accurate f0 (fundamental frequency / pitch)
estimates most of the time, but is sometimes off by a factor of N:1 or 1:N
where N is an integer; it means that it's prone to pick up on harmonics, and
sometimes even sub-harmonics (I'm not sure how that makes sense, but it does
happen). MPM has some fine-tuning parameters, but none of them really solves
the problem. MPM uses a NSDF (Normalized Square Distance Function) which is
similar to auto-correlation, but looking at NSDF plots suggests that the
problem can't easily be solved with the NSDF alone; it outputs maxima at delays
where the "self-similarity" is highest, and these delays can be directly
translated into frequencies, but sometimes the best candidate (highest maximum)
corresponds a harmonic or sub-harmonic rather than f0.
However, harmonics in a monophonic signal are equally spaced in frequency; if
f0 is 100hz, you'll also see spectrogram peaks at 200hz, 300hz, 400hz, and so
on. If the MPM error factor is 2:1 or 3:1, it'll report f0=200hz or
f0=300hz rather than the correct answer (f0=100hz). The spectogram analysis
goes through a static list of likely 1:N and N:1 candidates and finds the
best match. The spectogram analysis does not attempt to guess f0 on its own
because the spectogram is rather low in resolution (a real-time requirement).
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Alpha software: it hasn't seen any heavy duty usage yet
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f0estimates are noisy when signal-to-noise is low. This could probably be solved with filtering (at the expense of latency of course) -
It's bad at detecting low frequencies (below 50-100hz?). This is due to low spectrogram resolution. More testing (bass guitars!) is probably needed to figure out exactly how bad, or not bad, it is. But consider that the spectrogram has 512 bins @ 12khz (internal sample rate); this corresponds to a bin size of about 12hz (12000/512/2), and you need a couple of bins to detect a peak...
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There's room for optimizations! NSDF calculation could probably be vectorized (SIMD). Auto-correlation (which is similar to NSDF) can be optimized using Discrete Fourier Transforms (
O(n log n)instead ofO(n^2)), but my maths is not nearly dope enough to figure out whether it's possible with NSDF too?
Look in the pptool and fungame sub-directories.
Placed into the public domain / cc0 licensed. Uses old FFTPACK Fortran code ported to C, and placed into public domain by Monty of xiph.org (see http://www.netlib.org/fftpack/fft.c)