Parameterized Resampling Time-Frequency Transform

Abstract

Many signals contain multiple components with time-varying instantaneous frequencies (IFs) which share a common trajectory trend, such as machinery vibration signals, speech signals, and biomedical signals. To analyze this kind of signals and achieve high time-frequency resolution, we propose a method called parameterized resampling time-frequency transform (PRTF transform) in this paper. Adapting the idea of the general parameterized time-frequency transform (GPTF transform), we use a parameterized kernel to represent a resampling function and further construct time-varying and time-invariant resampling operators to eliminate IF variations and relocate IF positions. These operators can improve the energy concentration of multiple components simultaneously in the time-frequency representation (TFR). Typical kernel functions containing the polynomial function and Fourier series are provided for different kinds of signals. A corresponding kernel estimation method is proposed to detect the shared trend of IFs by utilizing multiple components and to recursively approximate kernel parameters. Both numerical simulations and practical experiments show the effectiveness of the proposed method in improving the time-frequency resolution of TFRs for non-stationary multi-component signals.