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Harmonic Decomposition of Audio Signals with Matching Pursuit

Rémi Gribonval 1, 2 Emmanuel Bacry 1
2 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : We introduce a dictionary of elementary waveforms, called harmonic atoms, that extends the Gabor dictionary and fits well the natural harmonic structures of audio signals. By modifying the "standard" matching pursuit, we define a new pursuit along with a fast algorithm, namely, the fast harmonic matching pursuit, to approximate N-dimensional audio signals with a linear combination of M harmonic atoms. Our algorithm has a computational complexity of O(MKN), where K is the number of partials in a given harmonic atom. The decomposition method is demonstrated on musical recordings, and we describe a simple note detection algorithm that shows how one could use a harmonic matching pursuit to detect notes even in difficult situations, e.g., very different note durations, lots of reverberation, and overlapping notes.
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Rémi Gribonval, Emmanuel Bacry. Harmonic Decomposition of Audio Signals with Matching Pursuit. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2003, 51 (1), pp.101--111. ⟨10.1109/TSP.2002.806592⟩. ⟨inria-00576203⟩



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