Non-iterative waveform deconvolution using analytic reconstruction filters with time-domain weighting

A new deconvolution approach is described for reconstructing fast step-like or impulsive signals that have been measured with a sampling oscilloscope for which an impulse response estimate is available. The approach uses analytic reconstruction filters to control noise amplification, and a new non-iterative filter optimization that is based on a calculated "indicated error" function that is similar in shape to the true error. The new method aids in reporting uncertainties of the deconvolution results and it permits the use of time-domain weighting to optimize the measurement of different waveform features. The performance of the proposed approach is compared with that of the Error Energy/Regularization approach that is currently popular.