A statistical instantaneous frequency estimator for high-concentration time-frequency representation

Abstract

The instantaneous frequency (IF)-based post-processing methods, synchrosqueezing and synchroextracting, can accurately characterize the time-varying frequency and amplitude of multi-component nonstationary signals. However, the window's length needs to be a tradeoff between time-frequency (TF) localization and mode separation. To broaden the limitation of window's length on TF localization, this study theoretically proposes a statistical IF estimator (SIFE) to extract the IFs and concentrate the short-time Fourier transform (STFT) spectrum. First, we introduce a frequency filter associated with the window function and convolve it with STFTs to define an inner product space, in which the IF trajectories of multi-component signals can be better highlighted with low dependence on the window function. Then, the SIFE is derived from a macroscopic perspective in the inner product space rather than in the STFT space as the previous post-processing method does. Finally, the STFT energies are significantly concentrated by extracting only the TF coefficients at all IFs or reassigning the TF coefficients to the respective IFs. Numerical examples demonstrate that the SIFE is superior to previous methods in extracting IFs and concentrating TF energies.