Reproduce “Time delay embeddings to characterize the timbre of musical instruments using Topological Data Analysis: a study on synthetic and real data” on OpenResearch
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About this paper
Gakusei Sato, Hiroya Nakao, Riccardo Muolo
Researchers from the Institute of Science Tokyo systematically investigated how time delay embedding parameters influence Topological Data Analysis (TDA) for characterizing musical timbre. They identified specific time delays (T_0/2 and T_0/4) that optimally highlight integer and non-integer harmonics, providing a quantifiable topological feature that distinguishes instrument timbres across synthetic and real-world audio from the NSynth dataset.
Key insights
- Topological Data Analysis (TDA), when applied with Time Delay Embeddings (TDE), demonstrates high sensitivity to subtle harmonic structures, including integer, detuned, and non-integer components.
- The selection of the time delay parameter (τ) in TDE is critical, as it profoundly influences the geometric and topological features extracted by TDA for timbre characterization.
- Optimal time delays exist for specific harmonic types: τ ≈ T_0/2 (half the fundamental period) is effective for integer harmonics, while τ ≈ T_0/4 (or 3T_0/4) is optimal for non-integer harmonics or noise.
Summary by alphaXiv.
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