Alias-Free Periodic Signal Analysis using Efficient Rate Nonuniform Sampling Sets

In many applications such as signal integrity checking of hardware prototypes or determining dynamic behavior of wideband amplifiers etc. analysis of periodic radio signals with high accuracy is desired. The straight forward approach is to sample the signal to be analyzed with twice its highest harmonic content. But as fundamental frequencies are often far into the MHz range its harmonics may well span into the upper MHz or even GHz range. This leaves two possibilities: first, obey the sampling theorem and sample at that rate. But ADCs able to sample in the GHz range are expensive, power hungry and offer 6 to 8 bits maximum. Sometimes, this is not an option at all. Second, try to live with under sampling accepting alias frequencies in baseband. As long as aliased harmonics do not overlap this presents an acceptable solution. If they overlap, however, nothing can be done once the signal is sampled. But there is one more option presented in this paper, namely the possibility of deliberate nonuniform sampling. If the sampling set is chosen in a convenient way, mostly offered by an additive random sampling (ARS) scheme, this opens up promising possibilities to extend the alias-free processing range into the far MHz or even GHz region.