Wavelets for sparse representation of music

Abstract

When using a discrete wavelet transform or a wavelet packet for obtaining a sparse representation of music-signals the first question that arises is which wavelet filter/mother wavelet to use. The sparseness is a measure of how fast the DWT coefficients decay, and we are interested in obtaining a representation where the energy of the signal is concentrated in a few of the DWT coefficients. It is well-known that the decay of the DWT coefficients is strongly related to the number of vanishing moments of the mother wavelet, and to the smoothness of the signal. We present the result of applying two classical families of wavelets to a series of musical signals. The purpose is to determine a general relation between the number of vanishing moments of the wavelet and the sparseness of the DWT coefficients, when applied to music signals.