Self-matched extracting wavelet transform and signal reconstruction

Abstract

Time-frequency (TF) analysis method provides a powerful tool to analyze non-stationary signals. However, for strongly time-varying signals, how to characterize the time-varying features of signals accurately, how to achieve a highly concentrated TF representation, and how to reconstruct signals with high accuracy are still challenging tasks. In this paper, in order to analyze strongly amplitude-modulated and frequency-modulated signals, we introduce an accurate instantaneous frequency (IF) estimator, further propose a high-resolution TF analysis method and three high-accuracy reconstruction methods. Firstly, we present signal parameter, chirp rate and IF estimation from the wavelet transform of Gaussian amplitude-modulated linear chirp model. Based on this, we introduce the self-matched extracting wavelet transform (SMEWT), which improves the energy concentration of TF representation, by only retaining TF information related to the IF of the signal. Furthermore, the signal parameter, chirp rate and IF estimation lead to accurate signal reconstruction formulas. In this regard, we provide a theoretical analysis and comparison of SMEWT reconstruction, and present two hybrid reconstruction methods of signal. It is well known that the reassignment method can improve the readability of the TF representation, but it cannot reconstruct the signal. It is worth mentioning that one of the proposed hybrid reconstruction methods is a combination of the reassignment method and deduced reconstruction formula, which not only captures the flavor and philosophy of the reassignment method, but also uses a hybrid way in signal reconstruction. Finally, simulated and real signals are employed to confirm the effectiveness of the proposed methods by comparing with some classical TF analysis methods.