ITERATIVE TECHNIQUES FOR THE SOLUTION OF FREQUENCY-DOMAIN FILTER SETS LARGE-ARRAY SIGNAL AND NOISE ANALYSIS
Abstract
Computation of high-resolution wavenumber spectra includes the solution of a set of Hermitian equations. This set of equations has the form of a least-squares multichannel frequency-domain filter design equation which can be expressed in vector-matrix notation as Ha = b, where H = n x n nonsingular Hermitian power spectral matrix; b = n x 1 known complex column vector of output power spectra; and a = n x 1 unknown complex column vector of filter weights. This report investigates three techniques of solving for the n x 1 unknown complex column vector of filter weights: the method of conjugate gradients, steepest-descent method, and exact-inverse method. The object is to determine the accuracy and computational complexity of each technique. Analysis of the methods available for the numerical solution of the frequency-domain multichannel filter-design problem yields two major conclusions. The exact inverse equation is by far the most satisfactory method for designing high- resolution filter sets from single transform data (a rank-one matrix of data). The exact inverse equation can be used to update the inverse of a spectral matrix for adaptively tracking nonstationary noise fields. Such information would be required to do Baysian location in a correlated noise field (for example, at the subarray level).
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 22, 1968
- Accession Number
- AD0835359
Entities
People
- Peter R. Fenner
Organizations
- Texas Instruments