Parametric Time-Frequency Representations

  • Y. Grenier
Part of the International Centre for Mechanical Sciences book series (CISM, volume 309)


This text describes parametric time-frequency representations, called here reliefs. After an analysis of the properties expected for such a relief, the classes of nonstationary signals are studied. One observe several equivalences between various definitions. This permits to define the class for which the concept of relief will be valid: the class of harmonizable nondegenerate signals. Two reliefs are presented in details, one defined by Priestley for oscillatory signals, the other defined by Tjøstheim using a commutation relation between two operators representing time and frequency. A third relief is also discussed: the rational relief. It is more adequate and simpler to use for ARMA signals. The estimation of these reliefs is also considered, through time-dependent ARMA modelling.


Impulse Response Commutation Relation Complex Exponential Rational Similitude Nonstationary Signal 
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© Springer-Verlag Wien 1989

Authors and Affiliations

  • Y. Grenier
    • 1
  1. 1.Ecole Nationale Supérieure des TélécommunicationsParisFrance

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