Dual dynamic kernel filtering: Accurate time-frequency representation, reconstruction, and denoising

Abstract

Time-frequency analysis plays a critical role in characterizing non-stationary signals such as electrocardiograms (ECG), where both spectral and temporal details are paramount. In this study, we introduce Dual Dynamic Kernel Filtering (2DKF) for time-frequency decomposition, emphasizing how kernel selection influences signal representation, reconstruction accuracy, and overall filtering performance. To overcome the limitations associated with signal-dependent single-kernel methods, we propose an innovative Dual hybrid kernel strategy that adaptively integrates multiple kernel functions to capture a wide array of signal characteristics. This approach significantly improves temporal alignment via Dynamic Time Warping (DTW), robustly preserves signal distributions as evidenced by quantile-quantile (QQ) plot analyses, and maintains high frequency fidelity during the filtering process. Extensive experimental comparisons against traditional discrete wavelet transform (DWT) and S-transform filtering, conducted under varying noise conditions, including synthetic noisy ECG with white noise, colored noise (brown and pink), and naturally noisy ECG, demonstrate that our dual hybrid kernel method substantially enhances robustness and consistency in signal reconstruction. Furthermore, we compare our approach with Recursive Multikernel Filtering (RMKF) technique for a benchmark nonlinear signal corrupted by structured noise, alongside wavelet and S-transform techniques. Evaluation metrics, including normalized mean square error (nMSE), root mean square error (RMSE) and correlation coefficients, confirm the superior performance of the proposed approach. These promising results underscore the potential of our method as a powerful tool for the time-frequency analysis of non-stationary signals, with significant implications for advanced ECG signal processing and other biomedical applications.