Tunable hyperbolic Cohen-class kernel for cross-term diminishing in time–frequency distributions. (1st March 2023)

• Record Type: Journal Article
• Authors: Martinez-Herrera, Ana L.; Ledesma-Carrillo, Luis M.; Ferrucho-Alvarez, Edna R.; Lopez-Ramirez, Misael; Rodriguez-Donate, Carlos; Cabal-Yepez, Eduardo
• Is Part Of: Mechanical systems and signal processing. Volume 186(2023)
• Publication Date: 2023-03-01
• Subjects: Cohen class -- Cross-terms suppression -- Time-frequency distributions -- Tunable hyperbolic kernel -- Wigner-Ville distribution; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2022.109850
• Languages: English
• ISSNs: 0888-3270

Abstract

Abstract: 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.