Abstract
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.
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Grenier, Y. (1989). Parametric Time-Frequency Representations. In: Longo, G., Picinbono, B. (eds) Time and Frequency Representation of Signals and Systems. International Centre for Mechanical Sciences, vol 309. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2620-2_4
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DOI: https://doi.org/10.1007/978-3-7091-2620-2_4
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