Non-Euclidean robustness measures for communications and signal processing.
We consider robustness with a global approach. Using differential geometry to calculate quantities such as maximum slope and Gaussian curvature, we demonstrate their use as indicators of robustness. These techniques are illustrated by example and show that analysis can be enhanced using stereo imagi...
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
2003.
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| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=765137301&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | We consider robustness with a global approach. Using differential geometry to calculate quantities such as maximum slope and Gaussian curvature, we demonstrate their use as indicators of robustness. These techniques are illustrated by example and show that analysis can be enhanced using stereo imaging as in the case of a simple two-dimensional parameter surface. We then develop the use of histograms to represent the distributions of these coordinate system invariant indicators of instability over regions defined by a common delta level of error. Two examples of the Huber-Strassen method are reviewed and discussed. In an effort to enhance our understanding of robustness and make possible a more complex response criterion than the worst case scenario truncation scheme offered by the Huber-Strassen method, we explore the necessity for and the possibilities of a more global view. The concepts of parameter surface, performance surface, maximum slope, and the use of stereo imaging are developed. In stereo imaging we present the concept of a "constant-horizontal" viewing plane, for any point of view, relative to the object of interest, to avoid the disorientation of rotation. A three-dimensional example is used to both justify the global view and to compare visualization methods that will be the focus of future work. In this example the parameter and performance surfaces as well as the surface of maximum slope are created and visually inspected using stereo imaging. Several surface representation techniques are presented and the concept of a global view is discussed. The method of sampling is considered as a further problem, especially in higher dimensions and for regions of high convolution. We list various problems and give reasons for using a random number generator to sample an unknown surface using a cubical grid. An expression for Gaussian curvature is developed and the use of histograms of these quantities is implemented for error level instead of local surface structure. We then present an extensive set of case studies employing all the above methods that demonstrate the use of these techniques in higher dimensions. |
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| Item Description: | Vita. "Major Subject: Electrical Engineering". |
| Physical Description: | xv, 155 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilm Inc. |
| Bibliography: | Includes bibliographical references (leaves 153-154). |