Novel methods for spectral analysis

R. Roy, B. G. Sumpter, G. A. Pfeffer, S. K. Gray, D. W. Noid

Research output: Contribution to journalReview articlepeer-review

59 Scopus citations

Abstract

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(ω) for many-body systems, semiclassical transition frequencies, overtone linewidths, and resonance energies of the time-dependent Schrödinger equation for few-body problems.

Original languageEnglish
Pages (from-to)109-152
Number of pages44
JournalPhysics Reports
Volume205
Issue number3
DOIs
StatePublished - Jun 1991

Funding

Research for D.W.N. and B.G.S. was sponsored by the Division of Materials Sciences, Office of Basic Energy Sciences, U.S. Department of Energy, under contract DE-ACO5-840R21400 with Martin Marietta Energy Systems, Inc. G.A.P. wishes to thank the University of Nebraska at Omaha Committee on Research for his designation as a Research Fellow. S.K.G. acknowledges support from the National Science Foundation and Office of Basic Energy Sciences, Division of Chemical Sciences, U.S. Department of Energy under contract no. W-31-109-ENG-38. Finally, we wish to acknowledge the excellent secretarial help of Mrs. Ceci Steele.

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