Guotong Zhou, ``Random Amplitude and Polynomial Phase Modeling of Nonstationary Processes Using Higher-order and Cyclic Statistics,'' Ph.D., Department of Electrical Engineering, University of Virginia, Charlottesville, VA, November 1994.
Advisor: Georgios B. Giannakis

In this dissertation we study cyclostationary processes, in particular we treat coupled/uncoupled and random/constant amplitude harmonics, as well as polynomial phase signals with time-varying amplitudes. The latter reduce to damped harmonics in their high-order instantaneous moment domains. Since (almost) periodicity is present, the resulting Fourier Series coefficients produce spectral lines and peak-picking procedures can be undertaken to yield parameter estimates. The first part of the dissertation deals with harmonically coupled tones which is a symptom attributed to system nonlinearities. Important issues such as suppression of additive (non)Gaussian noise and single record phase coupling detection are clarified. In the second part, we thoroughly study random amplitude modulated harmonics that appear in Doppler radar and underwater acoustics applications. Several parameter estimation schemes are devised which tradeoff statistical with computational efficiency, and/or high resolution. Performance analysis results such as large sample variance expressions and Cramér-Rao bounds are also provided. Lastly, we investigate polynomial phase signals with time-varying amplitudes and their application in time-varying modeling of nonstationary voiced speech. Comprehensive computer simulations illustrate our theoretical results.

For more information contact: Prof. G. B. Giannakis, Department of Electrical Engineering, University of Virginia, Charlottesville, VA 22903-2442; email: georgios@virginia.edu. The dissertation is available via anonymous ftp at: spirit.ee.virginia.edu, under directory /pub/zhou.