Deconvolution of Acoustic Emission and Other Causal Time Series

A new technique, root projection (RP), is given for quantitative deconvolution of causal time series in the presence of moderate amounts of noise. Deconvolution is treated as a well-conditioned but underdetermined problem and a priori information is employed to obtain comparable noise reduction to that achieved by singular value decomposition (SVD) techniques while providing more accurate frequency information about the inverse. Two detailed examples arc given. The first gives noise analysis for alternate methods for deconvolution with a Gaussian kernel. The second example presents a model acoustic emission transducer calibration problem with typical noisy and incomplete output data. This example is treated by the use of a robust cross-cutting algorithm combining both the RP and SVD methods.