Sampling a broad band sparse spectrum without anti-aliassing filters

A broad band sparse spectrum has a number of narrow bands with significant levels of energy. These bands lie at integer multiples of the carrier frequency. There is no energy except in these bands. Such spectra occur when, for example, a) prior to modulation, a carrier is not a perfect sinusoid; or, b) a modulated carrier passes through any single-valued nonlinearity such as clipping, dead-space, rectification, or unsymmetrical amplification. Such spectra are normally prepared for sampling by an anti-aliasing filter which effectively eliminates from the spectrum all but the baseband. It is, however, possible to find a low sampling frequency such that there is no aliasing to a selected band about the origin, without using an anti-aliasing filter.