Parametric Time-Frequency Representations

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 Tjostheim 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.

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