Tikhonov Regularization in Pulse Signal Processing for Oscilloscope Measurements

Abstract

A model for oscilloscope measurements has been developed and the broadband pulses waveform recovering and regularization methods have been proposed. In practice due to the influence of noise and measurement uncertainty, input signal recovery requires equations that are ill-posed to be solved, thus regularization was used. We have chosen a stabilizing function and have found a number of regularization parameters to describe a recovery filter. A mathematical simulation and an experimental verification have been conducted to confirm that recovery of a pulse waveform with a bandwidth increased by 1.5 times is performed with an increase in the noise root mean square (RMS) value of a recovered signal by 1.5–3 times.