Dual-band signal reconstruction based on periodic nonuniform sampling at optimal sampling rate

A continuous-time multi-band signal with arbitrary spectral support can be reconstructed from its periodic nonuniform samples with the average sampling rate being arbitrarily close to the Nyquist-Landau rate. However, according to the existing literature, the theoretical uniform sampling rate in each channel of a periodic nonuniform sampling system would be infinitely small. Also, the required number of channels would be impractically large, leading to numerous filters. Consequently, the corresponding systems would be too complicated for practical implementation. It is important to consider the tradeoff between sampling rate and complexity for such systems. In this paper, we address the exact recovery of the continuous-time dual-band signal from its periodic nonuniform samples at optimal sampling rate with a simple sampling and reconstruction system. Optimal sampling rate means that the sampling rate is reduced as close to the Nyquist-Landau rate as possible. Firstly, we develop constraints on the aliasing-free sampling frequency via first-order sampling. Then, sufficient conditions are given to reconstruct a uniform sequence from its periodic nonuniform samples at optimal sampling rate. The complexity of the proposed method is calculated, which is far less than that of the conventional scheme. Our method shows potential applications in orthogonal frequency-division multiplexing (OFDM) systems.