Fundamentals and waveform digitizer for non-uniformly sampled very fast burst-like signals

This is a paper describing theories and applications of digital spectrum analysis technique for nonuniformly sampled very fast burst like signals. The difficulty in sampling this kind of signals lies in the fact that the length of the signal is shorter than the affordable sampling time of current measuring instrumentation. The majority of the digital signal processing theories for nonuniformly sampled signals developed so far has always assumed random equivalent time sampling (or periodic nonuniform sampling) on signals with length much longer than the affordable sampling time. However, in practice, very fast burst-like signals occur in much scientific instrumentation and new digital spectrum analysis technique for nonuniformly sampled signals of this class is in demand. In this paper, we first derive a digital spectral representation of a nonuniformly sampled very fast burst-like signal, and then present a detailed spectrum analysis of a nonuniformly sampled sinusoid cycle. It is found that DFT of a nonuniformly sampled very fast burst-like signal can be represented in terms of the DFT of sampled data sequence obtained by sampling the signal at uniform rate. The signal-to-noise ratio of the sampling results is discussed. We then introduced a practical high-speed waveform digitizer for very fast burst-like signal, and indicated the theory developed in this paper can be applied to analyze the errors caused by timing jitter. Specifically, we analyze waveform digitizers which utilize delay line techniques to extend their capabilities with the current monolithic A/D converter technology. Theoretical results are confirmed by the simulation results with a very fast burst-like signal.