Sparse Representation of Musical Signals Using Source-Specific Dictionaries
The sparse representation of music sounds that consist of a single note at a time was examined in. Here, we extend the results to a more generic setting where music sounds may contain multiple notes (or chords) at the same time. The basic idea is to determine a set of elementary functions, called source-specific atoms, that efficiently capture music signal characteristics. We first decompose basic components of musical signals (i.e,, musical notes) into a set of Gabor atoms. Then, these Gabor atoms are prioritized according to their approximation capability to music signals of interest, and the prioritized Gabor atoms are used to synthesize source-specific atoms. To find a sparse representation for musical chords, we generate new atoms by regrouping source-specific atoms. This technique is applied to the approximation of real piano recordings, and its effectiveness in terms of good approximation capability and low computational complexity is demonstrated by experiments.