Large-domain discrete integration techniques for the wave equation as an aid in the calculation of propagation loss and the study of adaptive acoustic arrays

Abstract

This work is concerned with two inter-related problems: (1) the theory and application of algorithms for the discrete integration of the acoustic wave equation in large, multi-dimensional, variable-parameter domains and, (2) the automatic synthesis of adaptive acoustic arrays for the detection and estimation of received acoustic signals which are incident from such domains. It is shown that the steady-state integration of large domains may be partitioned into subdomain integrations for slowly-varying variable-parameter domains. A new method of integration based upon the Fast Fourier Transform is given. A new method for obtaining closed form coefficient expressions for the Fast Fourier Transform is shown and illustrated. The results of a general computer-display simulation program for the Widrow feed-forward algorithm are given. Several limitations and possible modifications to the Widrow procedure are given. The use of Kalman-type filters as an alternative method is introduced.