Adaptive time–frequency analysis based on autoregressive modeling

Abstract

A new adaptive method for discrete time–frequency analysis based on autoregressive (AR) modeling is introduced. The performance of AR modeling often depends upon a good selection of the model order. The predictive least squares (PLS) principle of Rissanen was found to be a good criterion for model order estimation in stationary processes. This paper presents a modified formulation of the PLS criterion suitable for non-stationary processes. Efficient lattice filters based on the covariance assumption are used to estimate the model parameters of all model orders less than some maximum order M. It is shown that the resulting complexity is no larger than M. The modified PLS criterion allows the model order to adapt to non-stationary processes and, in turn, compute adaptive AR based time–frequency representations (TFRs). Examples of time–frequency analyses for synthetic and bio-acoustical signals are provided as well as comparisons to classical time–frequency representations.