Sub-Nyquist Sampling of Bandpass Signals

The paper studies the process of folding the spectrum of a bandpass signal as a result of uniform sub-Nyquist sampling. Most publications on bandpass sampling consider optimal sampling to avoid aliasing. This article takes into account the possibility of aliasing of an arbitrary degree. The knowledge gained in this area is necessary for use in the study of multi-channel multi-frequency sampling, which provides the ability to restore a bandpass signal distorted by aliasing in channels. To make it possible to study the consequences of sub-Nyquist sampling at any ratio of sampling frequency and signal spectrum width and at any position of the signal on the frequency axis, at any degree of aliasing. Research is carried out on a plane whose axes are the lower bounding frequency of the signal band and the frequency itself. It is shown that the structure of this plane is a periodic continuation along both axes of a certain pattern. Therefore, it is enough to limit ourselves to studying only this pattern. The paper provides a structural analysis of this pattern and derives expressions that allow one to understand the consequences of sub-Nyquist uniform sampling for any of its parameters.