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Harmonic decomposition of audio signals with matching pursuit

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2 Author(s)
Gribonval, R. ; French Nat. Center for Comput. Sci. & Control (INRIA), IRISA/INRIA, Rennes, France ; Bacry, E.

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.

Published in:

Signal Processing, IEEE Transactions on  (Volume:51 ,  Issue: 1 )