Music Information Processing Using Continuous Speech Recognition Methods

我们将MIDI数据转化为乐谱的音乐节奏识别表述为HMM中的Viterbi路径搜索问题，其中隐藏状态和输出概率分别代表预期的音符值和实际演奏的音符长度。我们还通过将复调降为单音来解决复调音乐的节奏识别问题。采用分段k-means算法实现语音识别的节奏建模和节奏变化检测。通过定义给定旋律的输出、旋律背后的和弦的隐藏状态和和弦序列的随机语言模型，将给定旋律的和声（和弦寻找）表述为连续语音识别的同构问题。采用两步最大似然法开发了自动对位法，包括节奏设计和音高分配，并通过动态规划求解。在复调信号分析中，基于谐波约束下的k-means聚类算法，将分帧观测频谱建模为重叠的谐波结构，考虑到谐波结构中的分布式能量属于单个聚类，提出了谐波结构聚类算法。此外，通过引入聚类的概率分配，将k-means推广到em算法中，获得了更高的多音高估计性能。利用诸如AIC之类的信息标准，还启用了源的数量和八度位置。在复调信号分析中，提出了“频谱分析”方法。对数线性谱的傅里叶反变换称为“谱”。在对数尺度频率上，观测到的线性频谱被认为是基频分布密度和假设相同的多个音的谐波结构的卷积。这个想法开辟了一种新的信号处理能力。

We formulated music rhythm recognition for ranscribing MIDI data into music score as a Viterbi path search problem in HMM where hidden states and output probabilities represent the intended note values and actually played note lengths, respectively. We also solved rhythm recognition of polyphonic music by reducing polyphony intomonophony. Tempo modeling and tempo change detection were enabled with segmental k-means algorithm for speech recognition.Harmonization (chord finding) of given melodies was formulated as an isomorphic problem as continuous speech recognition by defining output by the given melody, hidden states by the chord behind the melody and stochastic language model by chord sequences. Automatic counterpoint was developed with a two-step maximum likelihood approach consisting of rhythm design and pitch allocation solved by dynamic programming.In polyphonic signal analysis, an algorithm named Harmonic-structured Clustering was developed based on the k-means clustering algorithm under harmonic constraint by modeling the framewise observed spectrum as overlapped harmonic structures and considering that the distributed energy in harmonic structure belongs to a single cluster. Furthermore, by introducing the probabilistic assignment to clusters, k-means was generalized into the EM-algorithm and attained higher performance of multi-pitch estimation. Utilizing an information criterion such as AIC, the number of sources and octave location were also enabled."Specmurt analysis" was proposed for polyphonic signal analysis. The inverse Fourier transform of linear spectrum with log-frequency was called "specmurt". Along log-scaled frequency, observed linear spectrum is regarded as convolution of distribution density of fundamental frequencies and harmonic structures of multiple tones which are assumed identical. This idea opened up a new signal processing capabilities.