By I. Pitas, A. N. Venetsanopoulos (auth.)

The functionality of a filter out is to remodel a sign into one other yet one more swimsuit­ capable for a given objective. As such, filters locate purposes in telecommunica­ tions, radar, sonar, distant sensing, geophysical sign processing, photograph seasoned­ cessing, and machine imaginative and prescient. a number of authors have thought of deterministic and statistical methods for the learn of passive, energetic, electronic, multidimen­ sional, and adaptive filters. lots of the filters thought of have been linear even supposing the speculation of nonlinear filters is constructing quickly, because it is clear via the varied learn papers and some really good monographs now to be had. Our study pursuits during this region created chance for cooperation and co­ authored courses in past times few years in lots of nonlinear clear out households defined during this ebook. due to this cooperation and a trip from John Pitas on a learn go away on the collage of Toronto in September 1988, the assumption for this ebook used to be first conceived. the trouble in writing one of these mono­ graph used to be that the realm appeared fragmented and no basic idea used to be on hand to surround the numerous other kinds of filters awarded within the literature. although, the similarities of a few households of nonlinear filters and the necessity for this kind of monograph supplying a extensive evaluation of the entire region made the professional­ ject necessary. the result's the booklet now on your arms, typeset on the division of electric Engineering of the college of Toronto in the course of the summer time of 1989.

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The first robust M-estimator proposed is the Huber estimator [2,7]. 1. 1: 'If function of the Huber estimator. 14) is not arbitrary. It results from the need to find an optimal M-estimator, in the minimax sense, when some observations outly from the symmetric model distribution F. Let us suppose that the outliers follow a symmetric distribution H. 15) where E is the degree of contamination with outliers. 19) NONLINEAR DIGITAL FILTERS 22 The Huber estimator is B -robust and possesses E• = 1/2. 14) tends to sign(x) and the Huber estimator tends to the median.

531-536, June 1980. S. V. Poor, "Robust Wiener-Kolmogoroff theory", IEEE Transactions on Information Theory, vol. IT-30, pp. 316-327, March 1984. A. Kassam, "Robust hypothesis testing and robust time series interpolation and regression", Journal of Time Series Analysis, vol. 3, pp. 185-194, 1982. M. J. Evans, "Robust signal and array processing", Proceedings of lEE, vol. 129, Pt. F, no. 4, pp. 297-302, Aug. 1982. [29] A. H. D. VandeLinde, "Robust detection of known signals", IEEE Transactions on Information Theory, vol.

7) TheM-estimator T,. 2): II X· i=t T,. 9). 7) is unbounded, thus the sample standard deviation is not B-robust and possesses e• = 0. It has been proven that a robustified version of the MLE of scale is given by [5, p. 1. 1: Shape of the robustified MLE scale estimator for normal distribution. 1 0-11) are the optimal B -robust M -estimators of scale. 483. 483 makes the estimator Fisher consistent for F = ci>. 483: T,. 12) is B-robust. In fact, it is proven in [5, p. 142] that the MAD estimator is the most B-robust estimator.

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