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USE OF EXPECTED ERROR IN THE DESIGN OF LEAST‐SQUARES OPTIMUM FILTERS *
Author(s) -
WIGGINS RALPH A.
Publication year - 1967
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1967.tb01789.x
Subject(s) - filter (signal processing) , filter design , autocorrelation , least squares function approximation , mathematics , noise (video) , adaptive filter , value (mathematics) , white noise , computer science , m derived filter , algorithm , control theory (sociology) , statistics , control (management) , estimator , artificial intelligence , image (mathematics) , computer vision
The design of least‐squares optimum filters is based upon minimizing a suitably defined error criterion. The expected value of this error is easily computable after the coefficients of the filter have been determined. When a particular filtering problem is specified, there are several parameters which are specifically not included in the optimization procedure. However, the magnitude of the expected error may be quite sensitive to these parameters. The examination of the relative values of the expected error for variations of these unspecified parameters may lead to a better definition of the filter problem. The parameters which are left unspecified by the general least‐square filter definition include: 1. The addition of white noise to the signal autocorrelation to stabilize the filter behavior. 2. The specification of the shape of the desired output of the filter. 3. The specification of the lag between the desired output and the input. Examples are given showing the relationship between these parameters and the value of the expected error.