Second-Order Statistics of Complex Signals

Propriétés du second ordre des signaux à valeurs complexes

Bernard Picinbono (1) , Pascal Bondon (1)

1 L2S - Laboratoire des signaux et systèmes

The second-order statistical properties of complex signals are usually characterized by the covariance function. However, this is not sufficient for a complete second-order description, and it is necessary to introduce another moment called the relation function. Its properties, and especially the conditions that it must satisfy, are analyzed both for stationary and nonstationary signals. This leads to a new perspective concerning the concept of complex white noise as well as the modeling of any signal as the output of a linear system driven by a white noise. Finally, this is applied to complex autoregressive signals, and it is shown that the classical prediction problem must be reformulated when the relation function is taken into consideration.

Domaines: Traitement du signal et de l'image [eess.SP]

Bernard Picinbono, Pascal Bondon. Second-Order Statistics of Complex Signals. IEEE Transactions on Signal Processing, 1997, IEEE Transactions on Signal Processing, 45 (2), pp.411 - 420. ⟨hal-01661242⟩