APPLICATIONS OF WAVELETS IN MUSIC The Wavelet Function Library

This thesis describes a set of tools for manipulating sampled signals using wavelet transforms, and outlines potential musical applications of this library. Wavelets improve on existing time frequency methods by representing signals as a sum of a single wavelet basis function at different positions and scales. A wavelet representation can be used to synthesize or transform sounds in a variety of interesting ways. While the use of wavelets in music has been discussed in several papers, there has been no easy way for composers of electro-acoustic music to experiment with wavelet transformations. In addition, there has been a need for a clear, non-technical presentation of wavelet theory, so that composers and other musicians can understand their potential usefulness. The thesis begins by examining relevant background material, including the theory and musical applications of various time and frequency based representations. The theory of wavelets is presented in more detail, along with some of the ways wavelets can be used in a musical context. The software library is then described at several levels of detail, including a brief tutorial and a set of examples. A set of appendices provide additional related information.