Flexible Wavelets for Music Signal Processing

Musical signals require sophisticated time-frequency techniques for their representation. In the ideal case, each element of the representation is able to capture a distinct feature of the signal and can be attached either a perceptual or an objective meaning. Wavelet transforms constitute a remarkable advance in this field and have several advantages over Gabor expansions or short-time Fourier methods. However, application of conventional wavelet bases on musical signals produces disappointing results for at least two reasons: (1) the frequency resolution of dyadic wavelets is one-octave, too poor for any meaningful acoustic decomposition and (2) pseudoperiodicity or pitch information of voiced sounds is not exploited. Fortunately, the definition of wavelet transform can be extended in several directions, allowing for the design of bases with arbitrary frequency resolution and for adaptation to time-varying pitch characteristic in signals with harmonic or even inharmonic structure of the frequency spectrum. In this paper we discuss refined wavelet methods that are applicable to musical signal analysis and synthesis. Flexible wavelet transforms are obtained by means of frequency warping techniques.