Conservation in signal processing systems

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2012

Author dc:creator

• Baran, Thomas A. (Thomas Anthony)

Advisor dc:contributor.advisor

• Alan V. Oppenheim.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/74991

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/74991