Time Evolving Spectra.
Abstract
Conventional spectral analysis methods do not describe the distribution of signal power in both time and frequency. Time dependent Fourier transforms are defined to extend the conventional theory to include instantaneous energy and power spectra for the past and future signal. These spectra are combined to define a generalized instantaneous power spectrum (GIPS) of the entire signal. The Sliding FFT method of calculating the GIPS is examined and the equivalence between the estimates for the real and analytic signal is shown. These methods are applied to nonstationary stochastic processes and the GIPS is shown as given by the Fourier transform of Loeve's generalized power spectrum of the process and to be the generalization of the Wiener-Kintchine theorem to nonstationary processes. It is also shown to represent the stationary process, the locally stationary process, and the deterministic process. In addition to the GIPS, i.e., the spectral mean, an expression for the spectral covariance, is given and the relationship between these functions and a GIPS estimate via an ensemble of Sliding FFT calculations is examined. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1976
- Accession Number
- ADA037151
Entities
People
- O. D. Grace
Organizations
- Naval Undersea Warfare Center