2026-09-18T18:54:30Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/749912022-01-13T07:54:29Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Alan V. Oppenheim.
Baran, Thomas A. (Thomas Anthony)
Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2012-11-19T19:33:06Z
2012-11-19T19:33:06Z
2012
2012
http://hdl.handle.net/1721.1/74991
813960071
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 205-209).
Conservation principles have played a key role in the development and analysis of many existing engineering systems and algorithms. In electrical network theory for example, many of the useful theorems regarding the stability, robustness, and variational properties of circuits can be derived in terms of Tellegen's theorem, which states that a wide range of quantities, including power, are conserved. Conservation principles also lay the groundwork for a number of results related to control theory, algorithms for optimization, and efficient filter implementations, suggesting potential opportunity in developing a cohesive signal processing framework within which to view these principles. This thesis makes progress toward that goal, providing a unified treatment of a class of conservation principles that occur in signal processing systems. The main contributions in the thesis can be broadly categorized as pertaining to a mathematical formulation of a class of conservation principles, the synthesis and identification of these principles in signal processing systems, a variational interpretation of these principles, and the use of these principles in designing and gaining insight into various algorithms. In illustrating the use of the framework, examples related to linear and nonlinear signal-flow graph analysis, robust filter architectures, and algorithms for distributed control are provided.
by Thomas A. Baran.
Ph.D.
214 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
Conservation in signal processing systems
Thesis
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<Abstract>Conservation principles have played a key role in the development and analysis of many existing engineering systems and algorithms. In electrical network theory for example, many of the useful theorems regarding the stability, robustness, and variational properties of circuits can be derived in terms of Tellegen's theorem, which states that a wide range of quantities, including power, are conserved. Conservation principles also lay the groundwork for a number of results related to control theory, algorithms for optimization, and efficient filter implementations, suggesting potential opportunity in developing a cohesive signal processing framework within which to view these principles. This thesis makes progress toward that goal, providing a unified treatment of a class of conservation principles that occur in signal processing systems. The main contributions in the thesis can be broadly categorized as pertaining to a mathematical formulation of a class of conservation principles, the synthesis and identification of these principles in signal processing systems, a variational interpretation of these principles, and the use of these principles in designing and gaining insight into various algorithms. In illustrating the use of the framework, examples related to linear and nonlinear signal-flow graph analysis, robust filter architectures, and algorithms for distributed control are provided.</Abstract>
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