Time delay embeddings to characterize the timbre of musical instruments using Topological Data Analysis: a study on synthetic and real data
Gakusei Sato, Hiroya Nakao, Riccardo Muolo
Timbre允许我们区分声音,即使它们具有相同的音高和响亮度,在音乐,乐器识别和语音中发挥重要作用。 传统方法,如频率分析或机器学习,往往忽略了声音的微妙特征。 拓扑数据分析(TDA)可以捕获复杂的模式,但它对音色的应用是有限的,部分原因是不清楚如何有效地代表TDA的声音。 在这项研究中,我们研究了不同的时间延迟嵌入如何影响TDA结果。 使用合成和真实的音频信号,我们识别时间延迟,增强谐波结构的检测。 我们的研究结果表明,与基本时期分数相关的特定延迟使TDA能够揭示关键的谐波特征,并区分整数和非整数谐波。 该方法对合成和真实乐器声音有效,为未来的作品开辟了道路,可以使用更高维度的嵌入和额外的持久性统计将其扩展到更复杂的声音。
Timbre allows us to distinguish between sounds even when they share the same pitch and loudness, playing an important role in music, instrument recognition, and speech. Traditional approaches, such as frequency analysis or machine learning, often overlook subtle characteristics of sound. Topological Data Analysis (TDA) can capture complex patterns, but its application to timbre has been limited, partly because it is unclear how to represent sound effectively for TDA. In this study, we investigat...
