Adaptive Harmonic Spectral Decomposition for Multiple Pitch Estimation
Adaptive Harmonic Spectral Decomposition for Multiple Pitch Estimation
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DOI：
10.1109/tasl.2009.2034186
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发表时间：
2010-03
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影响因子：
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通讯作者：
E. Vincent;N. Bertin;R. Badeau
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文献类型：
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作者：
E. Vincent;N. Bertin;R. Badeau
多音调估计包括在音频信号的短时间帧内估计音调声音的基本频率和显著性。该任务构成了音乐音频特定环境中的几个应用的基础。一种方法是使用诸如非负矩阵分解（NMF）的算法将信号的短期幅度谱分解成表示由时变幅度缩放的各个音高的基谱的总和。由于可能的乐器范围很广，基础频谱的先前训练通常是不可行的。然后必须从数据中自适应地估计适当的光谱，这可能由于过拟合问题而导致有限的性能。在本文中，我们模型的每个基础频谱的窄带频谱代表几个相邻的谐波分音的加权和，从而执行谐波和频谱平滑，同时适应每个仪器的频谱包络。我们推导出一个类似NMF的算法来估计模型参数，并在钢琴录音数据库上进行评估，考虑到窄带光谱的几种选择。该算法的性能类似于使用预训练钢琴谱的监督NMF，但与其他无监督NMF算法相比，音高估计性能提高了6%至10%。
Multiple pitch estimation consists of estimating the fundamental frequencies and saliences of pitched sounds over short time frames of an audio signal. This task forms the basis of several applications in the particular context of musical audio. One approach is to decompose the short-term magnitude spectrum of the signal into a sum of basis spectra representing individual pitches scaled by time-varying amplitudes, using algorithms such as nonnegative matrix factorization (NMF). Prior training of the basis spectra is often infeasible due to the wide range of possible musical instruments. Appropriate spectra must then be adaptively estimated from the data, which may result in limited performance due to overfitting issues. In this paper, we model each basis spectrum as a weighted sum of narrowband spectra representing a few adjacent harmonic partials, thus enforcing harmonicity and spectral smoothness while adapting the spectral envelope to each instrument. We derive a NMF-like algorithm to estimate the model parameters and evaluate it on a database of piano recordings, considering several choices for the narrowband spectra. The proposed algorithm performs similarly to supervised NMF using pre-trained piano spectra but improves pitch estimation performance by 6% to 10% compared to alternative unsupervised NMF algorithms.