Energy distribution for Coefficients of Redundant Signal Representations of Music

In this paper we investigate how the energy is distributed in the coefficients vector of various redundant signal representations of music signals. The representations are found using Basis Pursuit, Matching Pursuit, Alternating Projections, Best Orthogonal Basis and Method of Frames, with five different time-frequency dictionaries. We have applied these methods to music to examine their ability to express music signals in a sparse manner for a number of dictionaries and window lengths. The evaluation is based on the m-term approximation needed to represent 90 %, 95 %, 99 % and 99.9 % of the energy in the coefficients, also the time consummation for finding the representations are considered. The distribution of energy in the coefficients of the representations found using Basis Pursuit, Matching Pursuit, Alternating Projections and Best Orthogonal Basis depends mainly on the signal, and less on the minimization method, the dictionary and the length of the analysis window. The results indicate, that the sparseness of the representations do indeed tell something about the music signal, and this is an interesting subject for further investigation.