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

Authors:
Abdellah Kacha;Francis Grenez;Khier Benmahammed
Affiliations:
Service Ondes et Signaux, Faculté des Sciences Appliquées, Université Libre de Bruxelles, Av. F. D. Roosevelt 50, CP 165/51, B-1050 Brussels, Belgium;Service Ondes et Signaux, Faculté des Sciences Appliquées, Université Libre de Bruxelles, Av. F. D. Roosevelt 50, CP 165/51, B-1050 Brussels, Belgium;Département Electronique, Faculté des Sciences de l'Ingénieur, Université de Setif, Setif 19000, Algeria
Venue:
Signal Processing
Year:
2005

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Abstract

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.