Pitch recognition of musical notes on a smart phone
With limited resources such as slower CPUs, code size and RAM, how best to detect the pitch of a musical note, similar to what an electronic or software tuner would do?
Should I use:
- Kiss FFT
- FFTW
- Discrete Wavelet Transform
- autocorrelation
- zero crossing analysis
- octave-spaced filters
other?
In a nutshell, what I am trying to do is to recognize a single musical note, two octaves below middle-C to two octaves above, played on any (reasonable) instrument. I'd like to be within 20% of the semitone - in other words, if the user plays too flat or too sharp, I need to distinguish that. However, I will not need the accuracy required for tuning.
Answer
If you don't need that much accuracy, an FFT could be sufficient. Window the chunk of audio first so that you get well-defined peaks, then find the first significant peak.
Bin width = sampling rate / FFT size:
Fundamentals range from 20 Hz to 7 kHz, so a sampling rate of 14 kHz would be enough. The next "standard" sampling rate is 22050 Hz.
The FFT size is then determined by the precision you want. FFT output is linear in frequency, while musical tones are logarithmic in frequency, so the worst case precision will be at low frequencies. For 20% of a semitone at 20 Hz, you need a width of 1.2 Hz, which means an FFT length of 18545. The next power of two is 215 = 32768. This is 1.5 seconds of data, and takes my laptop's processor 3 ms to calculate.
This won't work with signals that have a "missing fundamental", and finding the "first significant" peak is somewhat difficult (since harmonics are often higher than the fundamental), but you can figure out a way that suits your situation.
Autocorrelation and harmonic product spectrum are better at finding the true fundamental for a wave instead of one of the harmonics, but I don't think they deal as well with inharmonicity, and most instruments like piano or guitar are inharmonic (harmonics are slightly sharp from what they should be). It really depends on your circumstances, though.
Also, you can save even more processor cycles by computing only within a specific frequency band of interest, using the Chirp-Z transform.
I've written up a few different methods in Python for comparison purposes.