YIN analyzed. Plots generated with gnuplot, numbers generated from the Go code in this directory.
The paper describing YIN is: YIN, a fundamental frequency estimator for speech and music by Alain de Cheveigné and Hideki Kawahara.
The sample used in the YIN analysis is a clip of F#4 classical guitar, taken from freesound.org (and chopped up with pydub and numpy).
As with last time, let's see how autocorrelation fails to give a good result:
The value of 44 lags here is produced with naive peak picking. Count the number of peaks and divide by their occurences.
This result is incorrect (as expected).
Difference function presented in the YIN paper:
The CMND function presented in the YIN paper:
There are two possible values of YIN pitch:
- 129 lags => pitch = 372.09Hz, produced by only using the Absolute Threshold function (described in the YIN paper)
- The value of 128.6 lags, shown in the plot, produced by applying Parabolic Interpolation to the result of the Absolute Threshold function, again as described in the YIN paper
Similarities with MPM:
- Normalization of the intermediate buffer
- Parabolic interpolation to choose a more refined lag perodicity
Differences with MPM:
- Not autocorrelation based
I implemented FFT YIN successfully in the main YIN code, following equation 7 from the YIN paper.
The YIN paper defines the formulation for the difference function, d_t, for a lag tau, as expressed in terms of the autocorrelation r_t:
d_t(tau) = r_t(0) + r_(t+tau)(0) - 2*r_t(tau)
The term r_(t+tau) was confusing for me, so in my code I substituted it for
d_t(tau) = 2*r_t(0) - 2*r_t(tau)
, where r_t(tau) is the same FFT-based autocorrelation function I use for MPM.
This is a big performance win for YIN from O(N^2) to O(NlogN), and all of the tests are still passing.
The accuracy didn't take a huge hit.
Time-domain YIN result:
$ time ./bin/stdin --sample_rate 44100 --algo yin <./samples/F-4_48000_classicalguitar.txt
Size: 174759 pitch: 342.271
closest note: F4 (349.2)
real 0m8.066s
user 0m8.020s
sys 0m0.004s
FFT YIN result:
$ time ./bin/stdin --sample_rate 44100 --algo yin <./samples/F-4_48000_classicalguitar.txt
Size: 174759 pitch: 342.238
closest note: F4 (349.2)
real 0m0.262s
user 0m0.216s
sys 0m0.043s
Time-domain YIN benchmark:
---------------------------------------------------------------
Benchmark Time CPU Iterations
---------------------------------------------------------------
BM_Yin_Sinewave/1024 60976 ns 60878 ns 11130
BM_Yin_Sinewave/4096 1002633 ns 1000951 ns 688
BM_Yin_Sinewave/32768 64198002 ns 64096428 ns 11
BM_Yin_Sinewave/262144 4125974701 ns 4114026064 ns 1
BM_Yin_Sinewave/1048576 67683358752 ns 67461192598 ns 1
BM_Yin_Sinewave_BigO 0.06 N^2 0.06 N^2
BM_Yin_Sinewave_RMS 0 % 0 %
FFT YIN benchmark:
---------------------------------------------------------------
Benchmark Time CPU Iterations
---------------------------------------------------------------
BM_Yin_Sinewave/1024 60657 ns 60202 ns 11223
BM_Yin_Sinewave/4096 241264 ns 239170 ns 2967
BM_Yin_Sinewave/32768 2077014 ns 2054092 ns 340
BM_Yin_Sinewave/262144 19811215 ns 19568974 ns 36
BM_Yin_Sinewave/1048576 95163598 ns 93849952 ns 7
BM_Yin_Sinewave_BigO 4.52 NlgN 4.46 NlgN
BM_Yin_Sinewave_RMS 3 % 3 %
CMNDF of clean viola clip (deg0):
CMNDF of unclean viola clip (deg4):
