In this paper, analysis and trans-synthesis of acoustic bowed string instrument recordings with new non-negative matrix factorization (NMF) procedure are presented. This work shows that it may require more than one template to represent a note according to time-varying behavior of timbre, especially played by bowed string instruments. The proposed method improves original NMF without the knowledge of tone models and the number of required templates in advance. Resultant NMF information is then converted into the synthesis parameters of the sinusoidal synthesis. Bach cello suites recorded by Fournier and Starker are used in the experiments. Analysis and trans-synthesis examples of the recordings are also provided. Index Terms—trans-synthesis, non-negative matrix factorization, bowed string instrument

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Note separation in music signal processing becomes difficult when there are overlapping partials from co-existing notes produced by either the same or different musical instruments. In order to deal with this problem, it is necessary to involve certain invariant features of musical instrument sounds into the separation processing. For example, the timbre of a note of a musical instrument may be used as one possible invariant feature. In this paper, a timbre estimate is used to represent this feature such that it becomes a constraint when note separation is performed on a mixture signal. To demonstrate the proposed method, a timedependent recursive regularization analysis is employed. Spectral envelopes of different notes are estimated and a modified parameter update strategy is applied to the recursive regularization process. The experiment results show that the flaws due to the overlapping partial problem can be effectively reduced through the proposed approach.

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