Stochastic resonance as a tool for smoothing time-frequency ridges in nonstationary signals

¹ Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, School of Mechanical and Electrical Engineering, China University of Mining and Technology - Xuzhou, 221116, China
² School of Computer Science and Technology, China University of Mining and Technology - Xuzhou, 221116, China
³ Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos Tulipán s/n, Móstoles, 28933, Madrid, Spain

Received: 19 May 2025
Accepted: 4 September 2025

Abstract

This study uncovers a novel role of stochastic resonance in enhancing the smoothness of time-frequency ridges in nonstationary signals. These signals combine rapidly shifting frequencies and amplitudes with irregular energy distributions. Moreover, environmental noise and overlapping components disrupt ridge continuity. To address these challenges, this study introduced a time-scale transformation coefficient into the bistable system and specifically discussed the system stability under nonstationary conditions. Meanwhile, two new evaluation metrics —the continuity index and the smoothness index— are introduced to assess the results quantitatively. Simulation results demonstrate that the proposed method significantly improves the smoothness of time-frequency ridges, thereby facilitating a more accurate analysis of nonstationary signal characteristics. This framework offers a novel paradigm for time-frequency analysis in the context of complex, nonstationary signals.