Tunable hyperbolic Cohen-class kernel for cross-term diminishing in time–frequency distributions

• Published in: Mechanical systems and signal processing 2023-03, Vol.186, p.109850, Article 109850
• Main Authors: Martinez-Herrera, Ana L., Ledesma-Carrillo, Luis M., Ferrucho-Alvarez, Edna R., Lopez-Ramirez, Misael, Rodriguez-Donate, Carlos, Cabal-Yepez, Eduardo
• Format: Article
• Language: English
• Subjects: Cohen class; Cross-terms suppression; Time-frequency distributions; Tunable hyperbolic kernel; Wigner-Ville distribution
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2022.109850

Nonstationary signals are found in many engineering applications. The analysis of nonstationary signals trough bi-dimensional functions allows tracing their time and frequency evolution. In this regard, energy-distribution representations allocate the analyzed-signal power over two description variables, time and frequency, and offer a large number of mathematical properties, such as an ideal infinite resolution in both domains. Unfortunately, energy-distribution representations generate cross terms for multi-component nonstationary signals, which might mislead the analysis interpretation. Cross-term effects can be lessened by applying an appropriate smoothing kernel; they distort the shape of auto terms at the same time. In this work, a novel tunable signal-independent hyperbolic kernel function is introduced for reducing cross-term effects, preserving valuable properties, during the analysis of multi-component nonstationary signals. Obtained results from computer-model and real-life cases of study validate and demonstrate the performance superiority of the proposed kernel function, in terms of cross-term suppression and time–frequency resolution, against the well-known and widely used the Choi-Williams distribution and the cone-shape distribution.