New results concerning stability of multidimensional digital filters.
Item
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Title
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New results concerning stability of multidimensional digital filters.
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Identifier
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AAI9315522
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identifier
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9315522
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Creator
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Zilovic, Mihailo Slobodan.
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Contributor
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Adviser: Leonid Roytman
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Date
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1993
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Language
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English
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Publisher
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City University of New York.
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Subject
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Engineering, Electronics and Electrical
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Abstract
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This thesis introduces three new fundamental results concerning stability of digital filters.;It is well known that in order for a 2-D digital filter to be BIBO stable, it is necessary that the denominator of the real rational filter transfer function is a discrete scattering Hurwitz polynomial (DSHP). A very simple concept for a test procedure for 2-D DSHP is presented first. The concept is based on the definition of the stability threshold (stability margin) and of the geometrical properties of the root loci of the polynomial under the test. Polynomials with a finite number of simple zeros on {dollar}T\sp2{dollar} are considered first. Necessary and sufficient conditions for such polynomials to be DSHP are presented. Also, for the case when a polynomial possesses multiple zeros on {dollar}T\sp2{dollar} the necessary condition for a polynomial to be a DSHP is derived. All the conditions are related to the values of a polynomial and its partial derivatives at the set of points on {dollar}T\sp2{dollar}.;The second result deals with a very special class of m-D (m {dollar}>{dollar} 2) first and higher order digital filters, which are proven to be asymptotically stable with the existence of the transfer function polar singularities in the closed unit polydisk. It is also proven that every 2-D digital filter with DSHP in the denominator of its rational transfer function is always asymptotically stable.;Finally, a new contribution to the very old, but still vital problem of the determination of the upper bound for polynomial zeros is given. The newly introduced bound is obtained through the application of Cauchy's bound theorem to a new polynomial, which is derived from the original one by way of an exponential transform.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
