PDF

Sparsity and Structure in Audio Signals Through Mixed Norms

Matthieu Kowalski

Sparse and structured signal expansions on dictionaries (i.e. a collection of elementary waveforms, called atoms) can be obtained through explicit modeling in the coefficient domain. For music signals, the most popular choice for dictionaries is the time-frequency representations. However, Heisenberg's uncertainty principle denies the possibility to have a good frequency resolution and a good time resolution at the same time. In order to represent both time structure such transients (for example, percusif sounds) and frequency structures such tonals (for example, musical notes played by a violin), one can choose an over-complete dictionary contained the two kinds of atoms. Then, on can seek relevant waveforms using a sparse representation of the signal.