Time-Frequency Analysis Tool - Radial Gaussian Kernel Time-Frequency Distribution

This paper introduces a time-frequency analysis tool - the Radial Gaussian Kernel Time-Frequency Distribution. To elaborate this concept further, we can explain how to avoid cross-terms in the time-frequency distribution plane. This requires eliminating mutual components while preserving auto-components in the ambiguity function domain. Achieving this objective involves designing an appropriate kernel function that matches the signal properties. The signal-adaptive radial Gaussian kernel time-frequency distribution is considered an excellent approach for time-frequency representation. From an implementation perspective, the radial Gaussian kernel can be implemented using a 2D Gaussian function in the ambiguity domain that decays radially from the origin. The kernel function parameters can be optimized based on signal characteristics using MATLAB functions like fmincon for constrained optimization. Key implementation steps include computing the ambiguity function, applying the radial Gaussian kernel as a filter, and performing the inverse Fourier transform to obtain the final time-frequency distribution. This method effectively suppresses cross-terms while maintaining high time-frequency resolution.