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A dedicated algorithm for sparse spectral representation of music sound ispresented. The goal is to enable the representation of a piece of music signal,as a linear superposition of as few spectral components as possible. Arepresentation of this nature is said to be sparse. In the present contextsparsity is accomplished by greedy selection of the spectral components, froman overcomplete set called a dictionary. The proposed algorithm is tailored tobe applied with trigonometric dictionaries. Its distinctive feature being thatit avoids the need for the actual construction of the whole dictionary, byimplementing the required operations via the Fast Fourier Transform. Theachieved sparsity is theoretically equivalent to that rendered by theOrthogonal Matching Pursuit method. The contribution of the proposed dedicatedimplementation is to extend the applicability of the standard OrthogonalMatching Pursuit algorithm, by reducing its storage and computational demands.The suitability of the approach for producing sparse spectral models isillustrated by comparison with the traditional method, in the line of the ShortTime Fourier Transform, involving only the corresponding orthonormaltrigonometric basis.

A dedicated greedy pursuit algorithm for sparse spectral representation of music sound