ASA 124th Meeting New Orleans 1992 October

4pMU8. Proportional-bandwidth high-resolution time-frequency representations for musical signals.

William J. Pielemeier

Gregory H. Wakefield

EECS Dept., Univ. of Michigan, 1301 Beal Ave., Ann Arbor, MI 48109

Time resolution, frequency resolution, and superposition requirements present a difficult trade-off in time-frequency representations for musical signals, both for individual instrument and ensemble analysis. Existing methods have significant limitations, particularly at low frequencies. A representation is developed in Cohen's class [L. Cohen, Proc. IEEE 77(7), 941--981 (1989)], which improves on existing methods for a large class of musical signals. The pseudo-Wigner distribution is extended to a proportional-bandwidth form well suited to the frequency resolution required for musical signals and musical frequency analysis, paralleling a constant-Q transform [J. Brown, J. Acoust. Soc. Am 89, 425--434 (1991)]. This has excellent resolution, but fails to provide even limited superposition. A kernel is designed for Cohen's class, based on a musical signal model, providing a limited superposition property while maintaining improved resolution when applied to this distribution. Favorable performance is demonstrated relative to constant-Q methods and spectrograms for both single instrument and ensemble cases, which are beyond the capabilities of phase vocoder and Fourier series-based methods.