A time-frequency distribution with parameter estimators for a musical signal model.

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 (Cohen, L., "Time-Frequency Distributions--A Review," 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 pitch analysis, paralleling a constant-Q transform. The traditional constant-bandwidth and the new constant-Q pseudo-Wigner distributions both have excellent resolution, but fail 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 either of these distributions. 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. The dissertation also develops frequency and power or amplitude estimators which operate on the constant-bandwidth version of the distribution. These parameterize the partial frequencies that comprise the signal model. They are based on Wigner distribution methods, and like the distribution themselves, do not assume that the signal is constant over an analysis window. The performance of these estimators is analyzed and compared with that of Fourier series and STFT methods for several musical cases, including attacks and transients of trumpet, vibraphone, and flute notes. In general, we find 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.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104014/1/9423288.pdfDescription of 9423288.pdf : Restricted to UM users only