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次へ: Multiphonic Case 上へ: HMM Using Rhythm Vectors 戻る: Rhythm Vector: a Tempo-Invariant

Rhythm Estimation: Search Problem in HMM


図: Rhythm vector as output of HMM




表: Rhythm recognition results [%]
a hidden state state transition output signal
$n$-tuples of note $(n+1)$-gram rhythm vectors


The two probabilistic models of rhythm vector and rhythm pattern can be combined in the HMM framework as shown in Table 1 and Fig. 2. This HMM gives the probability $P(X\vert Q)P(Q)$, where $P(Q)$ is the probabilistic model of rhythm score and $P(X\vert Q)$ is that of rhythm vectors and tempo fluctuation.

Rhythm estimation is to find the time sequence of states in the state transition network, $Q$, that gives the maximum a posteriori probability, $P(Q\vert X)$, given a sequence of observed note lengths series, $X$. Maximizing $P(Q\vert X)$ is equivalent to maximizing $P(X\vert Q)P(Q)$ according to Bayes theorem. The optimal sequence of states in HMMs is efficiently found through the well-known Viterbi algorithm. The sequence of intended notes $\hat{Q}$ is estimated in the maximum likelihood sense.


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次へ: Multiphonic Case 上へ: HMM Using Rhythm Vectors 戻る: Rhythm Vector: a Tempo-Invariant
平成16年3月25日