Harmonic Decomposition of Audio Signals with Matching Pursuit

Rémi Gribonval (1, 2) , Emmanuel Bacry (1)

1 CMAP - Centre de Mathématiques Appliquées
2 METISS - Speech and sound data modeling and processing

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.

Mots clés: audio signal processing; computational complexity; harmonic analysis; music; reverberation; signal detection; signal representation; Gabor dictionary; audio signals decomposition; elementary waveforms dictionary; fast algorithm; fast harmonic matching pursuit; harmonic atoms; harmonic decomposition; musical recordings; natural harmonic structures; note detection algorithm; note durations; overlapping notes; time-frequency representation

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Rémi Gribonval, Emmanuel Bacry. Harmonic Decomposition of Audio Signals with Matching Pursuit. IEEE Transactions on Signal Processing, 2003, 51 (1), pp.101--111. ⟨10.1109/TSP.2002.806592⟩. ⟨inria-00576203⟩