Harmonic Decomposition of Audio Signals with Matching Pursuit
Résumé
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
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