Bispectra and Phase Correlations for Chaotic Dynamical Systems
Abstract
The bispectrum is the natural third-order generalization of the power spectrum. It provides information about correlations between different Fourier components of a signal or image, and about the statistics of Fourier phase. A number of numerical and experimental studies of the bispectra of chaotic systems have been published. In this paper we present the first analytical calculations of the bispectra of chaotic dynamical systems. First, for a generalization of the classical sawtooth or Renyi map, we calculate the bispectrum using symbolic dynamics. Also, for intermittent systems, we calculate the bispectrum using the relationship between these systems and renewal processes. We review the results of these calculations, drawing some conclusions about the characteristic features of the bispectra of chaotic systems, and compare them with the features of some financial time series.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2000
- Accession Number
- ADP010900
Entities
People
- Allan K. Evans
- Mark D. London
- Stuart J. Nimmo
Organizations
- De Montfort University