NOVEL METHODS FOR SPECTRAL-ANALYSIS

In this review article, various techniques for obtaining estimates of parameters related to the spectrum of an underlying process are discussed. These techniques include the conventional nonparametric FFT approach and more recently developed parametric techniques such as maximum entropy, MUSIC, and ESPRIT, the latter two being classified as signal-subspace or eigenvector techniques. These estimators span the spectrum (of possible estimators in that extremes of a priori knowledge are assumed (nonparametric versus parametric) and extremes in the underlying model of the observed process (deterministic versus stochastic) are involved. The advantage of parametric techniques is their ability to provide very accurate estimates using data from extremely short time intervals. Several applications of these novel methods for frequency analysis of very short time data are presented. These include calculation of dispersion curves, and the density of vibrational states g(omega) for many-body systems, semiclassical transition frequencies, overtone linewidths. and resonance energies of the time-dependent Schrodinger equation for few-body problems.