Generalized Metaplectic Convolution-Based Cohen's Class Time-Frequency Distribution: Theory and Application

The convolution type of the Cohen's class time-frequency distribution (CCTFD) is a useful and effective time-frequency analysis tool for additive noises jamming signals. However, it can't meet the requirement of high-performance denoising under low signal-to-noise ratio conditions. In this paper, we define the generalized metaplectic convolution-based Cohen's class time-frequency distribution (GMC-CCTFD) by replacing the traditional convolution operator in CCTFD with the generalized convolution operator of metaplectic transform (MT). This new definition leverages the high degrees of freedom and flexibility of MT, improving performance in non-stationary signal analysis. We then establish a fundamental theory about the GMC-CCTFD's essential properties. By integrating the Wiener filter principle with the time-frequency filtering mechanism of GMC-CCTFD, we design a least-squares adaptive filter in the Wigner distribution-MT domain. This allows us to achieve adaptive filtering denoising based on GMC-CCTFD, giving birth to the least-squares adaptive filter-based GMC-CCTFD. Furthermore, we conduct several examples and apply the proposed filtering method to real-world datasets, demonstrating its superior performance in noise suppression compared to some state-of-the-art methods.