Spectral arrangement and other topics in first-order bandpass sampling theory

A problem of first-order bandpass sampling is that the indifferent disposition of the baseband spectrum may cause inconvenience in practical applications. To overcome it, we modify the first-order bandpass sampling theory according to the spectral arrangement of the sampled signal. We consider two situations on the arrangement of the shifted replicas of the bandpass signal spectrum: the normal and the inverse placement of the spectrum. The positive spectrum of the bandpass signal is placed in the lowest positive part of the sampled signal in the normal placement situation and in the lowest negative part in the inverse situation. The sampling frequencies are formulated in a cluster of lower and upper bounds in both situations, and robust sampling frequencies are given. Topics of the modified theory related to applications are addressed.