An algorithm for the removal of noise and jitter in signals and its application to picosecond electrical measurement

The accuracy of data recorded by many measurement systems is limited both by uncertainty in the measured value as well as by uncertainty in the trigger input to the system which controls when a measurement is taken. The former effect, which appears as noise on the underlying signal, is due, in part, to the sampling process and can often be reduced to an acceptable level by averaging many measurements. Noise on the trigger input gives rise to uncertainty in time between the trigger and the measurement points. The effect, known as jitter, causes a distortion of the signal which cannot be removed by averaging.We describe and analyse the effects of noise and jitter on a waveform, and an algorithm for removing, or reducing, these effects is presented. The work is motivated by an application in picosecond electrical and optoelectronic metrology where a laser pulse is measured by a system consisting of a photodiode and sampling oscilloscope. Here, since the length of the pulse is so short, perhaps only tens of picoseconds in duration, the effect of jitter is as pronounced as that of measurement noise. Results obtained by applying the algorithm to simulated data obtained from this application are presented.