Time-frequency-autoregressive random processes: modeling and fast parameter estimation

We present a novel formulation of nonstationary autoregressive (AR) models in terms of time-frequency (TF) shifts. The parameters of the proposed TFAR model are determined by "TF Yule-Walker equations" that involve the expected ambiguity function and can be solved efficiently due to their block-Toeplitz structure. For moderate model orders, we also propose approximate TF Yule-Walker equations that have Toeplitz/block-Toeplitz structure and thus allow a further reduction of computational complexity. Simulation results demonstrate that the TFAR model is parsimonious and accurate and that the performance of our parameter estimation methods compares favorably with that of Y. Grenier\´s method (see IEEE Trans. Acoust., Speech, Sig. Processing, vol.31, p.899-911, 1983).