Time-frequency analysis and instantaneous frequency estimation using two-sided linear prediction

This paper presents a new time-frequency distribution which uses a time-dependent two-sided linear predictor model. The current sample is estimated as a weighted sum of the past and future values. The two-sided linear prediction approach yields a smaller prediction error than that obtained by using the usual one-sided linear predictor model. To estimate the time-dependent coefficients of the two-sided linear predictor, these are expanded as a linear combination of a set of time functions basis which leads to an ensemble of equations of the type of Yule-Walker equations. The nonstationary power spectrum estimate is used as a time-frequency distribution to characterize the signal jointly in the time domain and the frequency domain. We show that two-sided prediction-based time-frequency distribution can discriminate two close components in the time-frequency plane that neither Choi-Williams distribution nor one-sided prediction-based time-frequency distribution are capable of resolving. Also, the proposed time-frequency distribution is used to estimate the instantaneous frequency. Examples show that the proposed approach outperforms the usual technique based on the nonstationary autoregressive model.