The Effects of Timing Jitter in Sampling Systems

Timing jitter generally causes a bias (systematic error) in the amplitude estimates of sampled waveforms. Equations are developed for computing the bias in both the time and frequency domains. Two principal estimators are considered: the sample mean and the socalled Markov estimator used in some equivalent-time sampling systems. Examples are given using both real and simulated data. I . INTRODUCTION HE PURPOSE of waveform sampling and digitizing T systems is to assign an amplitude value and a corresponding time of occurrence to each of a finite set of discrete points that define a waveform over a specified time epoch. In this paper we present an analysis of the effects of random errors in the time of occurrence of the waveform samples. Such errors are commonly called timing jitter. Since only the nominal sample times are known, the effect of timing jitter is to introduce random errors in the amplitude values which are assumed to correspond to the sample times. In general, estimates of the true waveform values that are based on the observed samples tend to be biased. This is generally true for any sampled waveform for which second and higher order derivatives exist. The bias depends on the statistical estimator that is used. We have examined estimators used in both real-time and equivalent-time sampling processes. While it is true that waveform estimates based on timejittered samples are generally biased, the power, or mean squared value of the waveform samples is asymptotically unbiased, provided that the jitter is uncorrelated with the waveform itself. Therefore, it will be shown that the power contained in the noise created by timing jitter is directly related to the bias described above. In recent years, timing jitter has been studied either directly [ l ] or indirectly [ 2 ] , [ 3 ] by several authors. In this work, we expand on the results using the mean in equivalent-time sampling given by Gans [ I ] , and include analyses of other estimation processes commonly used in equivalent-time sampling.