GENERALIZED COVARIANCES AND POWER SPECTRA FOR DISCRETE TIME SERIES.
Abstract
The object of the work presented here is to develop refined tools for characterizing discrete time series of finite duration. A fundamental assumption (certainly not unfamiliar) of periodicity is made so that the underlying time domain becomes a group in the mathematical sense. Group properties of this time domain, the additive group of integers modulo N, are used to motivate and unify the theory. For any complex valued function defined on the group, the usual autocovariance function of a single time variable is set up and then generalized to a family of functions of several time variables. The coefficients in the expansions of these functions in terms of the group characters are called the generalized power spectra. The latter can be simply expressed in terms of 'fourier moments' which are finite fourier transforms of powers of the given function of time. Also considered are the generalizations of these concepts to the case of several simultaneous time series.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1967
- Accession Number
- AD0659183
Entities
People
- R. P. Eddy