Applications of time-frequency analysis in musical acoustics

Abstract

The modal distribution (MD) is a member of Cohen’s class of time-frequency distributions that is designed specifically for signals that are well-modeled as the sum of time-varying partials, such as those generated by many musical instruments [W. Pielemeier and G. H. Wakefield, J. Acoust. Soc. Am. 99, 2382–2396 (1996)]. When combined with local operators on the time-frequency surface, MD analysis provides substantial improvement over techniques based on the spectrogram with respect to simultaneously resolving variations in amplitude and frequency. Furthermore, the analysis degrades gracefully as the acoustic signal varies from the specified model and, in several cases, can be extended to handle a broader class of signals. Examples drawn from violin vibrato, singing, and the piano are used to illustrate MD analysis and its extensions. Issues of system identification, time-varying signal models, and musical synthesis are also discussed on the basis of these examples. [Research supported by grants from the Ford Motor Company, the Office of Naval Research, the National Science Foundation, and the Office of the Vice President for Research at the University of Michigan.]