Interpretable Evaluation of Sparse Time–Frequency Distributions: 2D Metric Based on Instantaneous Frequency and Group Delay Analysis

Vedran Jurdana ()
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Vedran Jurdana: Department of Automation and Electronics, Faculty of Engineering, University of Rijeka, 51000 Rijeka, Croatia

Mathematics, 2025, vol. 13, issue 6, 1-24

Abstract: Compressive sensing in the ambiguity domain offers an efficient method for reconstructing high-quality time–frequency distributions (TFDs) across diverse signals. However, evaluating the quality of these reconstructions presents a significant challenge due to the potential loss of auto-terms when a regularization parameter is inappropriate. Traditional global metrics have inherent limitations, while the state-of-the-art local Rényi entropy (LRE) metric provides a single-value assessment but lacks interpretability and positional information of auto-terms. This paper introduces a novel performance criterion that leverages instantaneous frequency and group delay estimations directly in the 2D time–frequency plane, offering a more nuanced evaluation by individually assessing the preservation of auto-terms, resolution quality, and interference suppression in TFDs. Experimental results on noisy synthetic and real-world gravitational signals demonstrate the effectiveness of this measure in assessing reconstructed TFDs, with a focus on auto-term preservation. The proposed metric offers advantages in interpretability and memory efficiency, while its application to meta-heuristic optimization yields high-performing reconstructed TFDs significantly quicker than the existing LRE-based metric. These benefits highlight its usability in advanced methods and machine-related applications.

Keywords: time–frequency distribution; signal reconstruction; instantaneous frequency; entropy; compressive sensing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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