The theory of bandpass sampling

TLDR: The sampling of bandpass signals is discussed with respect to band position, noise considerations, and parameter sensitivity, and it is shown that the minimum sampling rate is pathological in that any imperfection in the implementation will cause aliasing.

Abstract: The sampling of bandpass signals is discussed with respect to band position, noise considerations, and parameter sensitivity. For first-order sampling, the acceptable and unacceptable sample rates are presented, with specific discussion of the practical rates which are nonminimum. It is shown that the minimum sampling rate is pathological in that any imperfection in the implementation will cause aliasing. In applying bandpass sampling to relocate signals to a base-band position, the signal-to-noise ratio is not preserved owing to the out-of-band noise being aliased. The degradation in signal-to-noise ratio is quantified in terms of the position of the bandpass signal. For the construction of a bandpass signal from second-order samples, the cost of implementing the interpolant (dynamic range and length) depends on Kohlenberg's sampling factor (1953) k, the relative delay between the uniform sampling streams. An elaboration on the disallowed discrete values of k shows that some allowed values are better than others for implementation. >