Module pitch_detection::detector::yin
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The YIN pitch detection algorithm is based on the algorithm from the paper YIN, a fundamental frequency estimator for speech and music. It is efficient and offers an improvement over basic autocorrelation.
The YIN pitch detection algorithm is similar to the McLeod, but it is based on a different normalization of the mean square difference function.
Let $S=(s_0,s_1,\ldots,s_N)$ be a discrete signal. The mean square difference function at time $t$ is defined by $$ d(t) = \sum_{i=0}^{N-t} (s_i-s_{i+t})^2. $$ This function is close to zero when the signal “lines up” with itself. However, close is a relative term, and the value of $d'(t)$ depends on volume, which should not affect the pitch of the signal. For this reason, the signal is normalized. The YIN algorithm computes the cumulative mean normalized difference function, $$ d'(t) = \begin{cases}1&\text{if }t=0\\ d(t) / \left[ \tfrac{1}{t}\sum_{i=0}^t d(i) \right] & \text{otherwise}\end{cases}. $$ Then, it searches for the first local minimum of $d'(t)$ below a given threshold.
Implementation
Rather than compute the cumulative mean normalized difference function directly, an FFT is used, providing a dramatic speed increase for large buffers.
After a candidate frequency is found, quadratic interpolation is applied to further refine the estimate.
The current implementation does not perform Step 6 of the algorithm specified in the YIN paper.