- Title
- Ergodic properties for multirate linear systems
- Creator
- Marelli, Damián; Fu, Minyue
- Relation
- IEEE Transactions on Signal Processing Vol. 55, Issue 2, p. 461-473
- Publisher Link
- http://dx.doi.org/10.1109/TSP.2006.885687
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Resource Type
- journal article
- Date
- 2007
- Description
- Stochastic analysis of a multirate linear system typically requires the signals in the system to possess certain ergodic properties. Among them, ergodicity in the mean and ergodicity in the correlation are the most commonly used ones. We show that multirate operations and time-variant linear filtering can destroy these ergodic properties. Motivated by this fact, we introduce the notions of strong ergodicity in the mean and strong ergodicity in the correlation. We show that these properties are preserved under a number of operations, namely, downsampling, upsampling, addition, and uniformly stable linear (time-variant) filtering. We also show that white random processes with uniformly bounded second moments are strongly ergodic in the mean and that mutually independent random processes with uniformly bounded fourth moments are jointly strongly ergodic in the correlation. The main implication of these results is that if a multirate linear system is driven by white (independent) random processes with uniformly bounded second (fourth) moments, then every signal in the system is strongly ergodic in the mean (correlation) and therefore ergodic in the mean (correlation). An application of these results is also discussed.
- Subject
- adaptive filters; adaptive signal processing; filtering; linear systems; maximum likelihood detection; nonlinear filters; random processes; signal analysis; signal processing; stochastic processes
- Identifier
- http://hdl.handle.net/1959.13/930433
- Identifier
- uon:10843
- Identifier
- ISSN:1053-587X
- Rights
- Copyright © 2007 IEEE. Reprinted from IEEE Transactions on Signal Processing. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Newcastle's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
- Language
- eng
- Full Text
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