A time-varying autoregressive (TVAR) approach is used for modeling nonstationary signals, and frequency information is then extracted from the TVAR parameters. Two methods may be used for estimating the TVAR parameters: the adaptive algorithm approach and the basis function approach. Adaptive algorithms, such as the least mean square (LMS) and the recursive least square (RLS), use a dynamic model for adapting the TVAR parameters and are capable of tracking time-varying frequency, provided that the variation is slow. It is observed that, if the signals have a single timefrequency component, the RLS with a fixed pole on the unit circle yields the fastest convergence. The basis function method employs an explicit model for the TVAR parameter variation, and model parameters are estimated via a block calculation. We proposed a modification to the basis function method by utilizing both forward and backward predictors for estimating the time-varying spectral density of nonstationary signals. It is shown that our approach yields better accuracy than the existing basis function approach, which uses only the forward predictor.

Hall Steven received his Ph.d in Economics in 2003. He is now working as professor at the university of Pennsylvania. He also received a B.S.C in philosophy in 2005.