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.