Time average estimation in the fraction-of-time probability framework
Authors:
- Dominique Dehay,
- Jacek Leśkow,
- Antonio Napolitano
Abstract
The problem of time average estimation is addressed in the fraction-of-time probability framework. In this approach, the observed signal is modeled as a single function of time rather than as a sample path of a stochastic process. Under mild regularity assumptions on temporal cumulants of the signal, a central limit theorem (CLT) is proved for the normalized error of the time average estimate, where the normal- izing factor is the square root of the observation interval length. This rate of convergence is the same as that obtained in the classical stochastic approach, but is derived here without resorting to mixing assumptions. That is, no ergodicity hypothesis is needed. Examples of functions of interest in communi- cations are provided whose time average estimate satisfies the CLT. For the class of the almost-periodic functions, a non normal limit distribution for the normalized error of the time average estimate can be obtained when the normalizing factor equals the observation interval length. The limit distribution, nev- ertheless, depends on the sequence adopted to perform the limit, a result that cannot be obtained in the classical stochastic approach. Numerical examples illustrate the theoretical results and an application to test the presence of a nonzero-mean cyclostationary signal is presented.
- Record ID
- CUTa3712e03b9864c66bafff3a5dc6b3197
- Publication categories
- ;
- Author
- Journal series
- Signal Processing, ISSN 0165-1684, e-ISSN 1879-2677
- Issue year
- 2018
- Vol
- 153
- Pages
- 275-290
- Other elements of collation
- tab.; wykr.; Bibliografia (na s.) - 290; Bibliografia (liczba pozycji) - 44; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 153
- Keywords in English
- time average, central limit theorem, fraction-of-time probability, functional approach, pseudo-random functions, almost-periodic functions
- DOI
- DOI:10.1016/j.sigpro.2018.07.005 Opening in a new tab
- URL
- https://www.sciencedirect.com/science/article/abs/pii/S0165168418302299 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 35
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTa3712e03b9864c66bafff3a5dc6b3197/
- URN
urn:pkr-prod:CUTa3712e03b9864c66bafff3a5dc6b3197
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.