Deconvolution of causal pulse and transient data

Abstract

The effects of the causality of a certain class of frequency domain filters that satisfy the Paley-Wiener criterion are discussed. Physical pulses and transients are causal functions of time; that is, their values are zero before t=0, the time at which they begin. Their measured waveform data are also causal. When deconvolution processing is applied to remove instrumentation errors and/or suppress the effects of noise, noncausal deconvolution methods may introduce unacceptable errors. The Nahman-Guillaume automatic deconvolution method is modified to ensure that causality is maintained in the deconvolution result. Examples which show the undesirable effects of noncausal methods and a means of eliminating such effects are given.<>