William J. Pielemeier Gregory H. Wakefield
EECS Dept., Univ. of Michigan, 1301 Beal Ave., Ann Arbor, MI 48109
Attacks and other phenomena that involve rapid amplitude and frequency variations over time present a difficult problem in the study of the dynamics of musical instrument modes. Fourier-series-based methods provide adequate time resolution under the conditions of signal periodicity but performance deteriorates rapidly with gross inharmonicity or large amplitude and frequency transients. Short-time Fourier transform (STFT) methods are most robust to these variations but provide limited resolution in time and frequency. In a previous paper, an alternative time-frequency representation that achieves better resolution than STFT methods, yet remains robust to conditions degrading Fourier series analysis, was presented [Pielemeier et al., J. Acoust. Soc. Am. 92, 2430(A) (1992)]. The present paper develops estimators for modal parameters of musical instruments based on this alternative time-frequency representation. The performance of these estimators is analyzed and compared with that of Fourier series and STFT methods for several musical cases, including the attack transients of trumpet, vibraphone, and flute notes. In general, it is found that the proposed estimators provide a more accurate portrait of the spectral dynamics of the musical signal than is possible using estimators based on the other two representations.