Energy concentration-based optimization of Gaussian window reassignment for time–frequency analysis, and its application in analyzing the non-stationary spectral and coherence of cardiovascular signals

The non-stationary nature of cardiovascular signals necessitates time-frequency (TF) methodologies that can precisely capture and characterize temporal variations in their frequency components. This study aims to explore the Non-Stationary Spectral Coherence (NSSC) characteristics between cardiovascular signals, including heart rate variability (HRV), respiratory (RESP), systolic arterial blood pressure variability (SABPV), and arterial pressure interval variability (APIV), of healthy young (yng) and elderly (eldy) subjects to understand cardiovascular control. For this analysis, an optimized Gaussian window reassignment (OptGWRS) TF technique is proposed to capture the characteristics of these signals. The parameters of the Gaussian window are optimized using a particle swarm optimization (PSO) algorithm to maximize the energy concentration of signals in the TF domain. Initially, the proposed method was validated using synthetic stationary and non-stationary time series data that flow the dynamic characteristics of cardiovascular signals within the low-frequency 0.04 to 0.15 Hz (LF) and high-frequency 0.15 to 0.4 Hz. (HF) band. The simulation results have demonstrated that the proposed method provided a more energy concentration and achieved a higher TF resolution. Furthermore, this method was applied to a real database. The simulation results have shown that the NSSC ranges between the HRV and APIV signals in the low frequency band has been significantly reduced (p = 0.000001) in the eldy group when compared to the yng group. In the LF band, the NSSC among HRV and RESP signals have not been influenced by aging and, in the HF band significantly reduced in the eldy compared to the yng group (p = 0.0125).