2ND-ORDER STATISTICS OF COMPLEX SIGNALS

The second-order statistical properties of complex signals are usually characterized by the covariance function, However, this is not suffic ient for a complete second-order description, and it is necessary to i ntroduce 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 perspect ive concerning the concept of complex white noise as well as the model ing of any signal as the output of a linear system driven by a white n oise. 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.