STUDIES IN OPTIMUM FILTERING OF SINGLE AND MULTIPLE STOCHASTIC PROCESSES

摘要

This report treats the design of discrete filters for the detection of signals caused by nuclear explosions on digitized seismic recordings. The theoretical aspects of filter design are treated, together with the setting up of the necessary formulas for realizing the filters on digital computers. Recursive computational schemes are presented for normal equations of Toeplitz form. For single processes the Levinson recursion for the extension of the prediction error operator and the extension of the general filter is developed, as well as the recursion to move the output origin. A corresponding development is given for multi-channel processes, as well as a development of the recursion to larger operators for the multi-dimensional processes. The prediction problem for single stationary time series is reviewed and the least square and Kolmogoroff solutions given. Extension is then made to the multiple case, the least squares equations set up and the Wiener-Masani factorization described. Heuristic use is made of the Hilbert space property of time series. A digital computer program for performing the Wiener-Masani factorization is discussed. (Author)