James W. Beauchamp
School of Music and Dept. of Elec. Eng., Univ. of Illinois at Urbana-Champaign, Urbana, IL 61801
Short time Fourier transform methods can be applied to the problem of modal analysis of percussion sounds, which are well known to contain inharmonic partials. One problem is that the Fourier transform is equivalent to a harmonically spaced filter bank, so it is not possible to position filter centers at arbitrary positions. Another problem is that, typically, percussion modes are closely spaced while their amplitudes change rapidly, which plays havoc with frequency versus time resolution limitations. For widely spaced modes, the first problem is solved by choosing the base analysis frequency to be an integral common divisor of the modal frequencies, so that each mode corresponds to a unique equivalent filter. When modes become too dense, they cannot be resolved, and bands of modes must be treated as indivisible entities in order to conserve the temporal behavior. For example, if a 20-ms time resolution is desired, modes no closer than 50 Hz can be resolved. Results and ramifications of these limitations for analysis of percussion instruments such as tubular bells, timpani, and cymbals will be presented and discussed.