Convolution Type of Metaplectic Cohen’s Distribution Time-Frequency Analysis Theory, Method and Technology

The conventional Cohen’s distribution can’t meet the requirement of additive noises jamming signals high-performance denoising under the condition of low signal-to-noise ratio, it is necessary to integrate the metaplectic transform for non-stationary signal fractional domain time-frequency analysis. In this paper, we embark on blending time-frequency operators and coordinate operator fractionizations to formulate the definition of the joint fractionizations metaplectic Wigner distribution (JFMWD), based on which we integrate the generalized metaplectic convolution to address the unified representation issue of the convolution type of metaplectic Cohen’s distribution (CMCD), whose special cases and essential properties are also derived. We blend Wiener filter principle and fractional domain filter mechanism of the metaplectic transform to design the least-squares adaptive filter method in the JFMWD domain, giving birth to the least-squares adaptive filter-based CMCD whose kernel function can be adjusted with the input signal automatically to achieve the minimum mean-square error (MSE) denoising in Wigner distribution domain. We discuss the optimal symplectic matrices selection strategy of the proposed adaptive CMCD through the minimum MSE minimization modeling and solving. Some examples are also carried out to demonstrate that the proposed filtering method outperforms some state-of-the-arts including the classical Gaussian filter, the Cohen’s distribution filtering methods with fixed kernel functions, the classical Wiener filter, the adaptive generalized linear canonical convolution-based filtering method, the adaptive Cohen’s distribution filtering method, the adaptive JFMWD-based Cohen’s distribution filtering method, and the adaptive generalized metaplectic convolution-based Cohen’s distribution filtering method in noise suppression.

I. Introduction

The conventional time-frequency distributions, such as Wigner distribution [1], [2], Choi-Williams distribution [3], [4] and Cohen’s distribution [5], [6], can’t meet the requirement of characterization and analysis of non-stationary signal refined features under complex sound, light, heat, electricity and magnetism environments. Integrating them with fractional domain time-frequency transforms, including fractional Fourier transform [7], [8], linear canonical transform [9], [10] and metaplectic transform [11], [12], makes contribution to the enhancement of refined information features characterization degree of freedom and analysis capability. It therefore becomes one of the research hotspots in the field of fractional domain signal processing [13], playing an important role in exploring fundamental theories, applied methods and technical principles of non-stationary signal fractional domain time-frequency analysis [14]. This is of great scientific significance for addressing practical problems encountered in radar, communications, sonar, biomedical and vibration engineering, and has bright application prospects in seismic exploration, electronic countermeasures, deep-sea detection, spectral imaging and ultrasonic inspection [15].