Digital spectra of nonuniformly sampled signals: fundamentals and high-speed waveform digitizers

A digital spectral representation of a nonuniformly sampled signal is derived, and a spectrum analysis of a nonuniformly sampled sinusoid is presented. It is found that the spectrum of a nonuniformly sampled sinusoid comprises uniformly spaced line spectra; in addition, the signal-to-noise ratio is obtained in closed form. The theories are then applied to analyze the harmonic distortion introduced in high-speed waveform digitizers due to time-base errors. Specifically, waveform digitizers are analyzed which utilize interleaving/multiplexing and random equivalent time-sampling techniques and the monolithic A/D converter technology to extend their capabilities. Theoretical results are confirmed by experimental results with a real waveform digitizer