Compensation of timing jitter-induced distortion of sampled waveforms

The presence of timing jitter between the trigger signal and the sampling strobe in an equivalent-time sampling oscilloscope causes distortion of the recorded waveform. Two methods exist to estimate the waveform from the jittered measurements. One method, called the median method, is based on the calculation of the point-by-point median of a large set of waveform measurements. It is shown here that this method is asymptotically biased if noise is present and if the waveform is nonmonotonic. Another method, called the pdf deconvolution method, is based on an estimation of the jitter probability density function and on a technique to deconvolve this density function from the average of all recorded waveforms. To estimate the jitter probability density function, it is assumed that the waveform has a part which can very well be approximated by a ramp during a time span which is smaller than the standard deviation. It is shown that a significant asymptotic bias is introduced by the method when this assumption is violated. A novel approach is proposed, based on a parametric model of the jitter probability density function, which results in an asymptotic unbiased estimate of the jitter probability density function. The method is experimentally verified, and it is explained why this method is especially useful when one is interested in the Fourier spectrum of the recorded waveform