Second-order bandpass sampling with direct baseband signal reconstruction

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.