Wavelets pp 164-171 | Cite as

Time-Frequency Representations of Broad-Band Signals

  • J. Bertrand
  • P. Bertrand
Part of the inverse problems and theoretical imaging book series (IPTI)


Joint time-frequency analyses were first devoted to the study of quasi-monochromatic signals for which familiar notions of time and frequency translations exist. In the axiomatic formulation of the problem, this situation has led to the strong requirement of covariance of the representation by the group of time and frequency translations. However, if the resulting representations are very interesting when applied to quasi-monochromatic signals, they lose meaning in the general case due to flagrant time localization anomalies. This latter point is illustrated in section II.


Wigner Function Affine Group Axiomatic Formulation Familiar Notion Frequency Translation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • J. Bertrand
    • 1
  • P. Bertrand
    • 2
  1. 1.LPTMUniversity Paris VIIParisFrance
  2. 2.ONERAChatillonFrance

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