Hyperbolic-tangent-function-based cyclic correlation: Definition and theory

Abstract Non-stationary, non-Gaussian signal processing is a challenging topic in signal processing research. Over the past decade, due to effectively addressing co-channel interference, cyclostationarity-based methodologies have found a wide range of applications, such as wireless communication, cognitive radio, and mechanical vibration monitoring. Despite offering a feasible scheme, the second and higher-order cyclostationarity-based methodologies suffer under non-Gaussian noise environments, particularly impulsive noise environments. In this paper, through studying the similarity measurement, nonlinear function, and mapping mode, we propose a novel methodology named hyperbolic-tangent-function-based cyclic correlation (HTCC) to address both Gaussian and non-Gaussian noises with a uniform expression. The idea is inspired by the fact that hyperbolic tangent function is not only a bounded function but also achieves a differential compression. In addition, the theoretical foundations of this novel method are introduced step by step, including the definition, property, and spectrum. A number of numerical experiments are carried out to compare the algorithm performance with existing competitive methods. The proposed method generally shows good effectiveness and robustness and can be utilized for denoising problems in signal processing.