System Identification Approach Applied to Jitter Estimation

A system identification approach is applied to estimate the jitter introduced by a high-frequency sampling oscilloscope. An extended model is proposed to describe the sample variance of a set of repeated (impulse response) measurements in the presence of additive and jitter noise. Then, the (weighted) least-squares and maximum likelihood estimator are introduced to estimate the standard deviation of this additive and jitter noise. First, results are shown based on simulations. These allow to test both the correctness of the implementations, to verify the ability to detect model errors and to study the effect of uncertainties on the input signal. Next, the jitter and additive noise standard deviation are estimated on real measurements by performing impulse response measurements using an Agilent 83480A sampling oscilloscope in combination with 83484A 50 GHz electrical plug-ins. Additional challenges, such as the conjugated effect of time base drift and time base distortion, are described and correctly taken care of, demonstrating the real power of a solid stochastical framework