Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy

MIDIT                               OFD                           CATS
Modelling, Nonlinear Dynamics       Optics and Fluid Dynamics     Chaos and Turbulence Studies
and Irreversible Thermodynamics     Risø National Laboratory      Niels Bohr Institute and 
Technical University of Denmark     Building 128                  Department of Chemistry
Building 321                        P.O. Box 49                   University of Copenhagen 
DK-2800 Lyngby                      DK-4000 Roskilde              DK-2100 Copenhagen Ø
Denmark                             Denmark                       Denmark


by Andrey L. Pankratov
Department of Physical Sciences
University of Salerno, Italy

MIDIT-seminar 478

Thursday April 27, 2000, 14.00 h
at MIDIT, IMM, Bldg. 305, Room 018, DTU,

Abstract: The determination of the spectral form of the oscillator signal may be considered in certain cases as the final goal of investigation of influence of random forces on an oscillator. The existence of a continuous part of the spectrum, even when it contains a quasi-monochromatic line, may restrict, e.g., the detection of small signals located close to the oscillator frequency. The necessity of a relatively exact knowledge of the spectrum is obvious in this case.

On the other hand, in a number of physical tasks the mechanism of broadening of the spectral line is considered on the basis of a random frequency modulation. Therefore, the determination of the spectral form of a signal with fluctuations in both amplitude and frequency is of independent importance.

A unified method for finding the shape and the linewidth of the signal, in general having correlated amplitude and frequency fluctuations, will be considered. The analysis is performed both for stationary and nonstationary fluctuations in amplitude and frequency. The frequency fluctuations will be considered in detail and the influence of correlated amplitude and frequency fluctuations on the form of spectral line will be described.