William J. Pielemeier
Sci. Res. Labs., Ford Motor Co., Dearborn, MI 48124
Rowena Guevara
Gregory H. Wakefield
Univ. of Michigan, Ann Arbor, MI 48109
Piano signals present both rapid attacks and compact clusters of inharmonic partials and are, therefore, good examples of worst-case signals for many techniques of short-time spectral representation. This paper demonstrates the application of a recently developed time-frequency distribution [Pielemeier and Wakefield, J. Acoust. Soc. Am. 92, 2430 (1992); J. Acoust. Soc. Am. 94, 1806 (1993)] to the analysis of piano and other challenging signals in musical acoustics. A step-by-step analysis of the piano signal using the time-frequency distribution is presented with caveats concerning data interpretation. Both visual representations and estimators for the instantaneous frequency and power of the partials are compared with those obtained from Fourier series and from short-time Fourier analysis. The type and source of artifacts associated with each method are highlighted and issues of computational complexity are discussed. When applied properly, the proposed time-frequency distribution provides better resolution of the temporal and spectral properties of these musical signals than is achieved with either alternative. [Work supported by the EECS Department and by the Ford Motor Co.]