Wideband Weyl symbols for dispersive time-varying processing of systems and random signals

Byeong Gwan Iem, Antonia Papandreou-Suppappola, G. Faye Boudreaux-Bartels

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We extend the narrowband Weyl symbol (WS) and the wideband P o-Weyl symbol (P o WS) 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 P o 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.

Original languageEnglish (US)
Pages (from-to)1077-1090
Number of pages14
JournalIEEE Transactions on Signal Processing
Issue number5
StatePublished - May 2002


  • Dispersive transformation
  • Narrowband and wideband systems
  • Nonlinear system
  • Nonstationary random process
  • Spreading function
  • Time-frequency representation
  • Time-varying system
  • Unitary transformation
  • Warping technique
  • Weyl symbol

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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