Paper Info
Title
Wideband Weyl symbols for dispersive time-varying processing of systems and random signals
Abstract
We extend the narrowband Weyl symbol (WS) and the wideband PO -Weyl symbol (PoWS) for dispersive time-frequency (TF) analysis of nonstationary random processes and time-varying systems. We obtain the new TF symbols using unitary transformations on the WS and the PO WS. For example, whereas the WS is matched to systems with constant or linear TF characteristics, the new symbols are better matched to systems with dispersive (nonlinear) TF structures. This results from matching the geometry of the unitary transformation to the specific TF characteristics of a system. We also develop new classes of smoothed Weyl symbols that are covariant to TF shifts or time shift and scaling system transformations. These classes of symbols are also extended via unitary warpings to obtain classes of TF symbols covariant to dispersive shifts. We provide examples of the new symbols and symbol classes, and we list some of their desirable properties. Using simulation examples, we demonstrate the advantage of using TF symbols that are matched to the changes in the TF characteristics of a system or random process. We also provide new TF formulations for matched detection applications
Year
DOI
Venue
2002
10.1109/78.995064
IEEE Transactions on Signal Processing
Keywords
Field
DocType
unitary transformation,signal representation,nonstationary random processes,quadratic time-frequency representations,dispersive time-varying processing,scaling system transformation,wireless communication channels,random processes,smoothed weyl symbols,time-varying systems,matched detection,random process,unitary transformations,dispersive channels,time shift transformation,unitary warpings,time-varying channels,random signals,simulation,dispersive shifts,narrowband weyl symbol,wideband weyl symbols,signal detection,nonlinear time-frequency structures,time-frequency analysis,dispersive time-frequency analysis,time frequency,frequency,geometry,time frequency analysis,signal processing,signal analysis,dispersion,nonlinear systems
Signal processing,Nonlinear system,Covariant transformation,Detection theory,Control theory,Mathematical analysis,Pure mathematics,Unitary transformation,Stochastic process,Time–frequency analysis,Time–frequency representation,Mathematics
Journal
Volume
Issue
ISSN
50
5
1053-587X
Citations 
PageRank 
References 
6
0.58
26
Authors
3
Name
Order
Citations
PageRank
Byeong-Gwan Iem1354.46
Antonia Papandreou-Suppappola223429.88
G. Faye Boudreaux-Bartels3192.67