Nonlinear Digital Filters: Principles and Applications - download pdf or read online
By I. Pitas, A. N. Venetsanopoulos (auth.)
ISBN-10: 1441951202
ISBN-13: 9781441951205
ISBN-10: 1475760175
ISBN-13: 9781475760170
The functionality of a clear out is to rework a sign into one other another swimsuit capable for a given goal. As such, filters locate functions in telecommunica tions, radar, sonar, distant sensing, geophysical sign processing, photograph professional cessing, and machine imaginative and prescient. a variety of authors have thought of deterministic and statistical methods for the learn of passive, lively, electronic, multidimen sional, and adaptive filters. many of the filters thought of have been linear even though the idea of nonlinear filters is constructing quickly, because it is clear via the various examine papers and some really expert monographs now on hand. Our study pursuits during this region created chance for cooperation and co authored courses up to now few years in lots of nonlinear clear out households defined during this booklet. due to this cooperation and a trip from John Pitas on a examine depart on the collage of Toronto in September 1988, the assumption for this ebook was once first conceived. the trouble in writing one of these mono graph used to be that the world appeared fragmented and no normal concept was once on hand to surround the numerous other forms of filters provided within the literature. even though, the similarities of a few households of nonlinear filters and the necessity for this sort of monograph delivering a huge evaluation of the entire zone made the professional ject worthy. the result's the publication now on your arms, typeset on the division of electric Engineering of the collage of Toronto through the summer season of 1989.
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Having defined the basics of order statistics, we proceed to the analysis of L-estimators. 7 L-ESTIMATORS L-estimators are based on order statistics. They are explicitly defined and easily calculated. Therefore, they have found extensive applications in digital signal and image processing, as will be shown in subsequent chapters. For example, median filtering is a widely used signal and image filtering technique that is based on L-estimators. In the following, we shall treat again the problem of location and scale estimation by using linear combinations of order statistics, in the general framework of robustness theory and influence functions.
Vol. 70, pp. 428-434. [10] R. B. D. Thesis, Princeton University, 1951. [11] D. M. Hawkins, "Fractiles of an extented multiple outlier test", J. Statist. Comput. 8, pp. 227-236, 1979. [12] V. Barnett, T. Lewis, Outliers in statistical data, Wiley, 1978. [13] J. L. , E. L. Lehmann, "Estimates of location based on rank tests", Ann. Math. 34, pp. 598-611, 1963. [14] L. A. D. Thesis, University of California, Berkeley, 1969. [15] D. A. Lax, An interim report of a Monte Carlo study of robust estimators of width, Technical report 93, series 2, Department of Statistics, Princeton University, 1975.
239. For the logistic distribution F (x)=[1+exp (-x)r1 , the R-estimator having the maximal efficiency is the Hodges-Lehmann estimator: x+x· Tn=med{T, i=1, .. n, j=1, .. 14) The Hodges-Lehmann estimator is related to the Wilcoxon test [4]. 293. 16) The median is related to the sign test [4]. 17) An alternative definition of the R-estimators is the following [3, p. 382]: Definition 2. 18) NONLINEAR DIGITAL FILTERS 34 to each of the n (n +1)/2 averages (xU> + x (k))/2, j<5Jc. The R-estimator Tn is the median of the discrete distribution that assigns probability wi" to each of the averages (xU> + x (k) )/2.
Nonlinear Digital Filters: Principles and Applications by I. Pitas, A. N. Venetsanopoulos (auth.)
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