Two-Band Signal Reconstruction from Periodic Non-uniform Samples

Abstract

The Shannon sampling theorem states the lowest sampling rate for the lowpass bandlimited signals. But for multiband bandlimited signals, it is inefficient to apply the Shannon sampling theorem. This is because the existence of gaps between successive bands makes it possible to realize sampling at a rate, which is lower than the Nyquist rate and lower-bounded by Nyquist-Landau rate. The Nyquist-Landau rate for multiband signals, can be attained via periodic nonuniform sampling. However, it is still very challenging to find the sampling rate for multiband bandlimited signals such that the average sampling rate approaches the Nyquist-Landau rate. In this paper, we aim to find the feasible range of sub-Nyquist sampling rate (such that uniform sampling at this rate causes no aliasing) for two-band signals without aliasing. In this paper, an efficient method to find the constraints on the sampling frequency of two-band signals is devised. The normal placement and inverse placement of the spectrum are considered. Guard bands are considered to increase the robustness of the proposed sampling scheme. Analytical study is provided to obtain the allowable region of sampling frequencies. The derived low sampling rate ensures a relaxed requirement in terms of sampling, processing, and memory.