Abstract Continuous-time lowpass signal can be perfectly reconstructed from its uniformly-spaced samples at the Nyquist rate. While sampling bandpass signal at the Nyquist rate usually needs higher rate than necessary, second-order sampling, which involves two uniform samplings of the signal at the same sampling rate with a time offset between the two sampling sets, can perfectly reconstruct a bandpass signal from sub-Nyquist rate samples. However, most findings in the literature focus on the theoretical analysis of second-order sampling without addressing its practical implementation. Moreover, bandpass signals are primarily restored at the original band positions. The frequency-translated version of signal is frequently required in typical applications. Conventional methods will recover the original signal first, then shift it to the band of interest. In this paper, a direct reconstruction of the second-order sampled arbitrary real-valued bandpass signal onto the baseband is discussed, and the uniformly-spaced samples at the baseband will be reconstructed. Reconstruction with frequency-shifting interpolants are designed. To enable second-order sampling in practice, the feasible time offsets are determined analytically. Also, the design of digital interpolants for reconstructing second-order sampled signals in baseband is included. Simulation results are included to confirm our theoretical calculations and show the superiority over several existing schemes.

中文翻译：

---

具有直接基带信号重建的二阶带通采样

摘要 连续时间低通信号可以以奈奎斯特速率从其均匀间隔的样本中完美地重建。虽然以奈奎斯特速率采样带通信号通常需要比所需更高的速率，但二阶采样涉及以相同采样速率对信号进行两次均匀采样，并且在两个采样集之间存在时间偏移，可以完美地重建带通信号：亚奈奎斯特速率采样。然而，文献中的大多数发现都集中在二阶采样的理论分析上，而没有解决其实际实施问题。此外，带通信号主要在原始频段位置恢复。典型应用中经常需要信号的频率转换版本。常规方法会先恢复原始信号，然后将其转移到感兴趣的波段。本文讨论了将二阶采样的任意实值带通信号直接重构到基带上，并重构基带上均匀间隔的样本。设计了具有频移插值的重构。为了在实践中实现二阶采样，可行的时间偏移是通过分析确定的。此外，还包括用于重建基带中二阶采样信号的数字插值器的设计。包括仿真结果以确认我们的理论计算并显示优于几种现有方案。并且基带上均匀间隔的样本将被重建。设计了具有频移插值的重构。为了在实践中实现二阶采样，可行的时间偏移是通过分析确定的。此外，还包括用于重建基带中二阶采样信号的数字插值器的设计。包括仿真结果以确认我们的理论计算并显示优于几种现有方案。并且基带上均匀间隔的样本将被重建。设计了具有频移插值的重构。为了在实践中实现二阶采样，可行的时间偏移是通过分析确定的。此外，还包括用于重建基带中二阶采样信号的数字插值器的设计。包括仿真结果以确认我们的理论计算并显示优于几种现有方案。