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This paper is concerned with the finite-time stochastic synchronization of a chaotic system without linear term and its application in secure communication based on synchrosqueezed wavelet transform (SWT). In order to improve the anti-jamming ability of chaotic systems and forecast the synchronization time, proper controllers are designed to achieve finite-time stochastic synchronization for the chaotic system with random perturbation. Based on the proposed chaotic synchronization systems, we present secure communication scheme about secondary encryption to enhance the level of security. Moreover, a novel SWT algorithm is introduced to correctly recover information signals at the end of the scheme. The SWT based scheme can decompose the information signal into a set of intrinsic mode type (IMT) function components. Then, instantaneous frequency and instantaneous amplitude of each IMT component are calculated through Hilbert transform. Simulation results confirm that both the synchronization approach and the security communication scheme are effective. For multi-component signals with adjacent frequency, the accuracy of recovered signals by SWT based on our scheme is higher than that recovered by the other time-frequency denoising methods.

A Novel Method of Realizing Stochastic Chaotic Secure Communication by Synchrosqueezed Wavelet Transform: The Finite-Time Case