Perfect reconstruction of digital spectrum from nonuniformly sampled signals

In this paper, we consider the probIem 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 AID converters [1]-[3]. An algorithm which allows one to reconstruct the digital spectrum perfectly is derived, and a numerical example is presented, The algorithm is noniterative and precise, and should prove to be useful in many applications.