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Estimation of fundamental frequencies in polyphonic music sound using subspace-based approach

Music is a sum of several instrumental sounds whose individual fundamental frequencies are based on the musical score. Reversely musical sound contains information about the score, such as the instruments played and their fundamental frequencies. Automatic identification of scores from the musical sound is called the automatic transcription. There are many items to be estimated; the type of instruments, fundamental frequency, and note. Among these, the fundamental frequency estimation problem (FFE) has been widely studied. It is extensively studied for more than thirty years and there are many algorithms for the estimation of mono-phonic sound and poly-phonic sound. In this paper we propose a new estimation method of musical sound using the subspace approach. Our algorithm can be used to estimate poly-phonic and poly-instrumental sounds. This subspace approach is based on the autocorrelation of sounds and the orthogonality property. First, we gather subspaces of various instruments with different fundamental frequency. We define the subspaces as sound manifold. Next, we compare sound manifold and the subspace of measurement musical sound. We use the noise subspace of measurement sound and apply a MUSIC-like algorithm which use the orthogonality property of the signal subspace and the noise subspace. We test our algorithm with MIDI signals and show good identification capability.