Perfect reconstruction of digital spectrum from nonuniformly sampled signals

In this paper, we consider the problem of reconstructing the digital spectrum from a set of nonuniformly spaced time samples of a signal. Specifically, we deal with the situation where the timing offsets of each sampling instance are known and have a periodic structure. Examples include the random equivalent time sampling system of a digital scope, and an ultra high speed waveform digitizing system with interleaved A/D converters [1-3]. An algorithm which allow one to reconstruct the digital spectrum perfectly is derived, and a numerical example is presented. The algorithm is non-iterative and precise, and should prove to be useful in many applications.