Estimation of Multilinear Signal Descriptors.
Technical rept. Jan 69-May 70,
JOHNS HOPKINS UNIV BALTIMORE MD CARLYLE BARTON LAB
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Measures of signal structure may be classified by means of the form of the signal-dependence they exhibit, and one important such class is that for which this dependence is multilinear. It includes the many bilinear and quadratic signal descriptors which have extensive application in correlation and spectral analysis. The subject of this report is the estimation of signal descriptors of this class from uncertain observations. The approach taken is the following. Procedures for obtaining the values of multilinear descriptors are first derived for the deterministic case where the only error is that due to the incomplete nature of the available signal measurements with respect to the class of signals postulated. The problem is then reconsidered for the more practical case where uncertainties, for which only a statistical description is possible, are present, and general expressions are derived for the estimation of the descriptors under these conditions. The expressions so obtained incorporate the data transformations previously derived for the corresponding deterministic problem. The dependence of the estimator structure on the processing procedure applicable in the absence of uncertainty is considered in greater detail in an important special case where an explicit solution may be obtained in closed form. Author