Optimal sampling functions in nonuniform sampling driver designs to overcome the Nyquist limit

In some applications the observed samples are inherently nonuniform. In contrast to that in this paper we take advantage of deliberate nonuniform sampling and perform DSP where the classical approaches leave off. For instance think about mobile communication or digital radio. Deliberate nonuniform sampling promises increased equivalent sampling rates with reduced overall hardware costs. The equivalent sampling rate is the sampling rate that a uniform sampling device would require in order to achieve the same processing bandwidth. While the equivalent bandwidth of a realizable system may well extend into the GHz range its mean sampling rate is usually in the MHz range. Current existing prototype systems achieve 40 times the bandwidth of a classic DSP system that would operate uniformly (cf. [Y. Artyukh, et al., Evaluation of Pseudorandom Sampling Process, 1997] and [Y. Artyukh, et al., virtual Oscilloscope of the DASP-Lab System 1997]). Throughout the literature on nonuniform sampling (e. g. [I. Bilinskis and A. Mikelsons, 1992], [F. Marvasti, 2001] and [J.J. Wojtiuk, 2000]) many sampling schemes have been investigated. In this paper the authors discuss a nonuniform sampling scheme that is especially suited to be implemented in digital devices, thus, fully exploiting state-of-the-art ADCs without violating their specifications. An analysis of the statistical properties of the algorithm is given to demonstrate common pitfalls and to prove its correctness.