An Efficient Forecasting Approach to Reduce Boundary Effects in Real-Time Time-Frequency Analysis

Adrien Meynard (1) , Hau-Tieng Wu (1, 2, 3)

1 Duke University, Department of Mathematics
2 Duke University, Department of Statistical Science
3 Mathematics Division, National Center for Theoretical Sciences

Time-frequency (TF) representations of time series are intrinsically subject to the boundary effects. As a result, the structures of signals that are highlighted by the representations are garbled when approaching the boundaries of the TF domain. In this paper, for the purpose of real-time TF information acquisition of nonstationary oscillatory time series, we propose a numerically efficient approach for the reduction of such boundary effects. The solution relies on an extension of the analyzed signal obtained by a forecasting technique. In the case of the study of a class of locally oscillating signals, we provide a theoretical guarantee of the performance of our approach. Following a numerical verification of the algorithmic performance of our approach, we validate it by implementing it on biomedical signals.

Mots clés: forecasting; time-frequency; boundary effects; nonstationarity

Domaines: Traitement du signal et de l'image [eess.SP]

Adrien Meynard, Hau-Tieng Wu. An Efficient Forecasting Approach to Reduce Boundary Effects in Real-Time Time-Frequency Analysis. IEEE Transactions on Signal Processing, 2021, 69, pp.1653-1663. ⟨10.1109/TSP.2021.3062181⟩. ⟨hal-03141062v2⟩