Second-order time-frequency synthesis of nonstationary random processes

We present timefrequency methods for the synthesis of finite-energy, nonstationary random processes. The energetic characteristics of the process to be synthesized are specified in a joint timefrequency domain via a timefrequency model function. The synthesis methods optimize the autocorrelation function of the process such that the process’ Wigner-Ville spectrum is closest to the given model function. An optional signal subspace constraint allows the incorporation of additional properties such as bandlimitation and also permits the reformulation of the synthesis methods in a discrete-time setting. The synthesized process is expressed either in terms of an orthonormal basis of the constraint subspace or via its Karhunen-Lohe expansion. An example involving the prolate spheroidal functions is given, and computer simulation results are provided.