2ND-ORDER TIME-FREQUENCY SYNTHESIS OF NONSTATIONARY RANDOM-PROCESSES

We present time-frequency methods for the synthesis of finite-energy, nonstationary random processes. The energetic characteristics of the p rocess to be synthesized are specified in a joint time-frequency domai n via a time-frequency model function. The synthesis methods optimize the autocorrelation function of the process such that the process' Wig ner-Ville spectrum is closest to the given model function. An optional signal subspace constraint allows the incorporation of additional pro perties such as bandlimitation and also permits the reformulation of t he synthesis methods in a discrete-time setting. The synthesized proce ss is expressed either in terms of an orthonormal basis of the constra int subspace or via its Karhunen-Loeve expansion. An example involving the prolate spheroidal functions is given, and computer simulation re sults are provided.