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<p>An ROC curve has been constructed that determines the characteristics of a signal receiver with a fractally dependent radar signal detection coefficient using continuous wavelet decomposition of signals from the time domain into the frequency domain, and determining the fractal features using the generalized Hurst exponent. This ROC curve is located in the upper left corner of the graph, indicating a high true positive rate and confirming the correct determination of positive results. The curve constructed using the fractal features of the classical Hurst exponent is located along the diagonal of the graph, confirming the low quality of detection. It is shown that for 2D images of wavelet spectra, Minkowski dimension (the relationship between the maxima of fractal dimension and noise power) can be used as a fractal feature. This made it possible to identify spectrum images. The threshold for such identification is determined by compariing of the self-coherence of the series of wavelet coefficients from which the specified images are generated.</p>

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Constructing ROC Curves of Radar Signals with Detection Threshold Based on the Hurst Exponent

  • 期刊论文

  • 发表日期：

    2025年9月30日

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  • Yu. Taranenko,
  • O. Oliinyk,
  • Y. V. Khomyak

摘要

An ROC curve has been constructed that determines the characteristics of a signal receiver with a fractally dependent radar signal detection coefficient using continuous wavelet decomposition of signals from the time domain into the frequency domain, and determining the fractal features using the generalized Hurst exponent. This ROC curve is located in the upper left corner of the graph, indicating a high true positive rate and confirming the correct determination of positive results. The curve constructed using the fractal features of the classical Hurst exponent is located along the diagonal of the graph, confirming the low quality of detection. It is shown that for 2D images of wavelet spectra, Minkowski dimension (the relationship between the maxima of fractal dimension and noise power) can be used as a fractal feature. This made it possible to identify spectrum images. The threshold for such identification is determined by compariing of the self-coherence of the series of wavelet coefficients from which the specified images are generated.