The achievement of spectral super-resolution sensing is critically important for a variety of applications, such as radar, remote sensing, and wireless communication. However, in compressed spectrum sensing, challenges such as spectrum leakage and the picket-fence effect significantly complicate the accurate extraction of super-resolution signal components. Additionally, the practical implementation of random sampling poses a significant hurdle to the widespread adoption of compressed spectrum sensing techniques. To overcome these challenges, this study introduces a generalized eigenvalue method that leverages the incoherence between signal components and the linearity-preserving characteristics of differential operations. This method facilitates the precise extraction of signal component parameters with super-resolution capabilities under sub-Nyquist sampling conditions. The proposed technique is founded on uniform sub-Nyquist sampling, which represents a true sub-Nyquist approach and effectively mitigates the complexities associated with hardware implementation. Furthermore, the proposed method diverges from traditional compressed sensing techniques by operating outside the discrete Fourier transform framework. This departure successfully eliminates spectral leakage and the picket-fence effect. Moreover, it substantially reduces the detrimental impacts of random sampling on signal reconstruction and hardware implementation, thereby enhancing the overall effectiveness and feasibility of spectral super-resolution sensing.

翻译：实现频谱超分辨率感知在雷达、遥感及无线通信等众多应用中至关重要。然而在压缩频谱感知中，频谱泄漏和栅栏效应等挑战显著增加了超分辨率信号分量精确提取的难度。此外，随机采样的实际实施对压缩频谱感知技术的广泛推广构成了重大障碍。为克服这些挑战，本研究提出一种广义特征值方法，该方法利用了信号分量之间的非相干性及微分运算的线性保持特性。该方法能够在子奈奎斯特采样条件下，以超分辨率能力精确提取信号分量参数。所提技术基于均匀子奈奎斯特采样，这是一种真正的子奈奎斯特方法，有效降低了硬件实现的复杂性。此外，本方法脱离了传统压缩感知的离散傅里叶变换框架，成功消除了频谱泄漏和栅栏效应。同时，该方法大幅降低了随机采样对信号重建和硬件实现的有害影响，从而提升了频谱超分辨率感知的整体有效性和可行性。