To enhance noisy linear frequency-modulated (LFM) signal processing capacity without increasing computational and parameters selective complexity, this study introduces the so-called kernel function-τ\tau-Wigner distribution (KF-τ\tau-WD) by combining the kernel function Wigner distribution (KFWD) with the τ\tau-Wigner distribution (τ\tau-WD). We obtain the computational complexity of the KF-τ\tau-WD through the computational complexity analyses of the KFWD and τ\tau-WD. We formulate its parameters selection strategy for noisy LFM signal processing in accordance with Heisenberg's uncertainty principles. Our theoretical results are also verified by numerical simulations.

中文翻译：

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核函数-$\tau$-与线性正则变换相关的维格纳分布


为了在不增加计算和参数选择复杂度的情况下增强噪声线性调频（LFM）信号处理能力，本研究通过结合核函数引入所谓的核函数-τ\tau-Wigner分布（KF-τ\tau-WD）函数维格纳分布 (KFWD) 与 τ\tau-Wigner 分布 (τ\tau-WD)。通过对KFWD和τ\tau-WD的计算复杂度分析，我们得到了KF-τ\tau-WD的计算复杂度。我们根据海森堡不确定性原理制定了噪声 LFM 信号处理的参数选择策略。我们的理论结果也通过数值模拟得到了验证。